In a glass measuring cup, heat the milk to 110 degrees F (40 degrees C) and stir in the sugar and yeast. If using active dry yeast, allow it to sit for 15 minutes for the yeast to activate. If using instant yeast, simply move on to the next step.

Mix the eggs and vanilla into the milk yeast mixture.

In the bowl of a stand mixer fitted with a dough hook, mix the flour and salt together. Pour the wet ingredients into the flour and mix on low-medium speed for about 3 minutes, or until it forms a ball around the hook.

Add in a few pieces of butter at a time, allowing them to fully incorporate before adding more. Once all of the butter is incorporated, turn the mixer up to medium-high speed and mix for 8-12 minutes. The dough will eventually pull away from the sides of the bowl and have a silky smooth texture with minimal stickiness. To check if the dough is ready, use the windowpane test - tear off a small piece and carefully spread it out to see if you can see the light through it without it tearing. If it tears, mix for another minute or two and check again.

Once the dough is ready, transfer it to a lightly greased bowl, cover, and allow to proof overnight (or at least 6 hours) in the fridge. Alternatively, you can let the dough rise in a warm place for about 1 hour or until doubled in size.

Place a large skillet over medium heat, and add the butter. Stir frequently with a rubber spatula until the milk solids have separated and darkened.

Add the apples and mix frequently for about 4-5 minutes until they have softened. Stir in the flour and continue to cook for 2-3 more minutes until the liquid has thickened. Remove from heat.

On a small baking sheet, spread the apples into an even layer and allow to cool completely. Alternatively, you can make the spiced apples the day before when you make the brioche, and chill them overnight.

Place a wire rack over a paper towel lined baking sheet. On a separate baking sheet, cut out 9 4” (10 cm) parchment squares for the donuts.

On a lightly floured surface, roll the dough out to ¼” (.5 cm) in thickness. Dust the dough with some extra flour. Using a fork, add the apples (reserving most of the sauce) to one half of the dough. Dust the apples with more flour, then fold the other half of the dough over on top. Using a bench scraper or large knife, cut the dough into approximately 1” (2.5 cm) pieces. Use your hands to gently toss the pieces to separate.

Cover the donuts and allow to rise for about 30 minutes or until nearly room temperature, but still slightly cool to the touch. When pressed with a finger, the dough will slowly spring back.

Once proofed, give the fritters one final squeeze to ensure they stick together, then use the parchment squares to gently lower 2-3 donuts into the hot oil. Fry the donuts for 2 ½ minutes on the first side, then flip over and fry for an additional 2 ½ minutes.

Transfer the donuts to the wire rack. Wait a couple minutes for the oil to come back up to 355 degrees F (180 degrees C), then continue frying the donuts.