Brown Butter Espresso Dobos

Place the butter in a light-colored saucepan over medium heat. Cook, stirring frequently and scraping the bottom of the pan, until the butter melts and begins to foam. Continue cooking until the milk solids turn golden brown and the butter smells nutty. Immediately remove from the heat.
227 grams salted butter browned to 186 grams 150 grams for the custard and 36 grams for the sponge
Measure out 150 grams of the liquid brown butter for the custard. Transfer the remaining butter, including all the browned bits, to a measuring cup and reserve for the sponges. You should have about 36 grams remaining.

Stir together the espresso with just enough water to make it dissolve.
1 Tbsp espresso powder, 1/2 Tbsp water to dissolve the coffee
Whisk the egg yolks and sugar together in a medium bowl. Slowly pour in the 150 grams of brown butter while whisking constantly.
4 egg yolks, 67 grams granulated sugar, 150 grams browned butter - the liquid part; reserve solids for the sponge
Then return the mixture to the saucepan used to brown the butter, making sure all the remaining browned bits have been scraped into the measuring cup.
Cook over low heat, stirring continuously, until the custard reaches at least 170°F and thickens slightly, leaving visible trails.
Transfer the custard to a bowl, whisk in the dissolved coffee and press plastic wrap directly onto the surface. Allow to cool, then refrigerate until completely chilled. I refrigerated mine for several hours.

Preheat the oven to 400°F convection. Grease three 13 × 18-inch sheet pans with baking spray and line with parchment paper.
Add the oil, egg yolks and vanilla to the measuring cup containing the reserved brown butter and browned bits. There is no need to whisk the egg yolk mixture together.
80 mL canola oil or any kind, 36 grams reserved brown butter including the browned bits, 1/2 tsp vanilla bean powder or 1 Tbsp of vanilla bean paste, 6 large egg yolks
In the bowl of a stand mixer fitted with the whisk attachment, beat the egg whites, water and sugar on high speed until thick and fluffy.
2 Tbsp water, 100 grams granulated sugar, 6 large egg whites
Pour in the egg yolk mixture, scraping all the browned bits into the batter, and beat for just a few seconds, until combined.
Scrape down the sides of the bowl. With the mixer on medium speed, add the flour in 3-4 increments. Scrape the bowl again and gently fold as needed until fully combined and no pockets of flour remain.
120 grams flour sifted
Divide the batter evenly among the three prepared pans, approximately 7 ounces per pan and spread it into a thin even layer.
Bake each sponge for approximately 6 minutes, rotating halfway through if needed for even browning. The sponges may be cooked through after about 4 minutes, but allow them to brown nicely so they do not remain gummy.
Allow the sponges to cool completely. Cut each sheet lengthwise into three equal strips to make nine long, skinny rectangles.

Using a stand mixer or hand mixer, beat the chilled custard with the Cool Whip and vanilla just until fully combined.
300 grams cool whip thawed, 2 tsp vanilla bean paste
Reserve one sponge strip for the caramel topping. Place another strip on a serving plate and spread with a layer of cream approximately as thick as the sponge.
Continue alternating sponge and cream, using the remaining seven strips and finishing with a layer of cream. Leave the reserved ninth strip off the cake.
Refrigerate the cake for several hours, until set.
Trim the edges of the chilled cake, then trim the reserved sponge strip to match. If decorating the outside, prepare the buttercream below.

Combine the 4 leftover egg whites and sugar in the metal bowl of a stand mixer and set over a saucepan of gently simmering water, making sure the bowl is not submerged in the water. Whisk continuously until the sugar has completely dissolved.
4 large egg whites, 200 grams granulated sugar
Transfer the bowl to the stand mixer fitted with the whisk attachment. Beat on high speed for approximately 10 minutes, until the meringue is thick, fluffy and no longer warm.
Stir together the espresso with just enough water to make it dissolve and set aside.
1 Tbsp espresso powder, 1/2 Tbsp water to dissolve the coffee
With the mixer running, add the butter a few tablespoons at a time. Once all the butter is incorporated, increase the speed to high and beat until the buttercream comes together and is smooth.
227 grams unsalted butter
Add the vanilla and dissolved coffee, if using, and beat until fully incorporated.
1 Tbsp vanilla bean paste
Frost the sides and top of the chilled cake as desired, reserving about one-third of the buttercream for piping around the caramel topping.

Place the reserved sponge strip on a cutting board lined with parchment paper.
Add the sugar to a saucepan and cook over low heat until melted and the color turns into amber.
200 grams granulated sugar
Remove from the heat and immediately pour over the reserved sponge, spreading into an even layer.
While the caramel is still hot, grease a knife with butter or oil and score the topping crosswise to mark individual portions. Reapply butter to the knife as needed.
Allow the caramel to set completely.
For easier slicing: Cut completely through the scored lines to separate the caramel-topped sponge into individual pieces, then arrange them on top of the cake.
For a cleaner appearance: Leave the caramel-topped sponge whole and place it directly on top of the cake. Slice through the scored lines when serving. This looks neater but can be more difficult to cut.
Pipe the reserved buttercream around it, if using.