Place the flour, yeast, 3 tablespoons sugar, and salt in the bowl of a stand mixer fitted with the hook attachment. Turn the mixer to low speed, add in the eggs and egg yolks, followed by the softened butter and water. 

Once they’re all combined, turn the mixer to medium-low speed and allow it to knead the dough for 10 to 15 minutes, or until the dough begins to peel itself away from the sides of the bowl and forms a ball around the hook attachment. 

If this doesn’t happen within the kneading time, the dough is too sticky; add 1 to 2 tablespoons (7 to 14 g) of flour and continue to knead until the dough comes together.

Test the strength of the dough by stretching a piece of dough between your fingers. The dough should stretch thin enough to let light through before tearing. 

Push the dough to one side of the bowl, grease the open side of the bowl, then repeat with the other side. Cover the bowl with plastic wrap. 

Place the bowl in a warm environment, in the sunlight or on a stovetop warming zone, and allow it to proof until it’s doubled in size; this may take anywhere from 1 to 2 hours.

Line two baking sheets with 16-20 4x4” parchment paper squares, and lightly flour a work surface. 

Once the dough has doubled in size and is really fluffy, punch it down and turn it over onto the prepared work surface,

Prepare for frying the donuts by lining two cooling racks with paper towels and spreading the 1 cup of sugar and cinnamon and/or vanilla powder in a bowl. 

Ten minutes before the donuts are done proofing, heat the oil in a large pot over high heat to about 360F (182C) on a candy thermometer, then lower the heat to medium. Use the thermometer to keep the oil within 10 degrees of 360F (182C).

Depending on the size of your pot, place two to four donuts in the oil at a time, being sure to leave space around them. Fry the donuts on each side, turning the donuts with a slotted spoon, for 1 to 2 minutes, or until they are browned.

If it is taking longer than 2 minutes to brown one side of the donut, increase the heat just a little. Work quickly, and avoid having an empty pot, so the oil doesn’t burn.

Place the fried donuts on the prepared racks. While they’re still warm, toss the donuts in the sugar. Serve warm or let them cool completely to room temperature if filling the donuts.

In a small or medium saucepan, whisk together the egg yolks and sugar until they're well combined. Add the salt and slowly pour in the milk while whisking.

When the mixture is smooth, cook it over medium-low heat while whisking continuously (but not super aggressively) for about 5 minutes, until it begins to thicken.

Once it begins to thicken, whisk aggressively for one more minute and then pour into a heat safe bowl. Stir in the butter until it's well combined.

Cover the surface of the custard with plastic wrap and refrigerate until it's completely cooled. Before adding to the whipped cream, whisk it to make it smooth again.

Once the custard has cooled, make the whipped cream.

Combine the cream and sugar in the bowl of a stand mixer, and use the whisk attachment to beat the mixture at medium speed until it thickens a bit, about 30 seconds.

Turn the speed up to medium-high, and whisk the cream until it reaches stiff peaks, about 1 minute.

Add the cooled custard to the whipped cream, and turn the mixer up to medium-high speed, beating just until the cream is fully combined.

Use a piping bag to pipe into the donuts and serve fresh.