In a large mixing bowl or with your stand mixer using the paddle attachment, combine the warm milk (I took mine out of the fridge and warmed in the microwave for about 1 minute and 20 seconds to reach the desired temperature) with the active dry yeast and sugar. Allow the mixture to sit without mixing for 5-10 minutes or until the mix is foamy and starts to smell like bread.

Once foamy, add the butter and egg and mix quickly to combine all ingredients, about 30 seconds.

Add 3 cups of flour and the salt and knead using the dough hook or your hands until the dough comes together. If you're using a hand mixer this will take about 3 minutes. If you're using your hands it will take longer, 5-10 minutes. Add the remaining 1/2 cup flour in increments until the dough is no longer too sticky. It should be slightly sticky to touch.

Once complete, grease a large bowl and place the dough inside and cover tightly with plastic wrap. Let rise in a warm place while making the pastry cream (directions below), or at least 15 minutes.

To fry the brioche doughnuts, line two large baking sheets with parchment paper and set aside. Moderately flour a clear work surface and roll the dough out to 1/2 - 3/4 inch thickness. Using a doughnut or circular cookie cutter, cut out 3-inch diameter rounds and arrange on the prepared baking sheet. Fill the sheet and cover with plastic wrap while finishing the rest of the dough. Repeat the process until the dough is cut out and all of the doughnuts are covered in plastic wrap.

In a heavy-bottomed large pot or deep fryer, heat a minimum of 2 inches of oil until a frying thermometer reaches 350°F, being careful not to allow it to get too hot. Working in batches of 3 or 4, use a slotted spoon to carefully place the doughnuts in the hot oil. Fry until golden brown, between 1 and 2 minutes per side, flipping only once. Transfer hot doughnuts to a wire rack to cool then make sure the oil returns to 350°F before frying the next batch. Let the doughnuts cool completely before filling with cream.

To fill the doughnuts, place the pastry cream in a pastry bag or plastic bag with the tip cut off. Insert a knife into the middle of the doughnut from the long end to create a hole. Place the tip of the pastry bag inside and fill the doughnut with cream until full.

In a medium bowl, whisk together the sugar, flour and salt. Add the egg yolks and whisk until thoroughly combined to create a thick paste and set aside.

Warm the milk in a saucepan over medium high heat until you start to see wisps of steam coming off the milk, just before it starts to boil. Pour a small amount of the hot milk into the eggs and whisk to combine to bring the temperature of the eggs up without them scrambling. Continue to pour the milk in slowly, whisking continually, until completely incorporated. Once mixed, pour the entire mixture back into the saucepan over medium heat. Whisk vigorously and constantly until the cream thickens. At first it will be very thin and frothy but will begin to thicken and turn to a pudding-like consistency after a few minutes. Pause periodically to see if the cream comes to a light boil. If you see bubbles it's done. Whisk a few more seconds and remove from the heat.

Using a strainer, pass the cream through to ensure any cooked eggs are removed. Cover the cream directly on the surface with plastic wrap and place in the refrigerator to cool completely while you fry the doughnuts.