Instructions

• In the bowl of a stand mixer, combine the instant yeast and warm water. Let sit about 10 minutes to dissolve the yeast.
• Add the sugar, salt, softened unsalted butter, whole egg, egg yolk, ½ teaspoon vanilla extract, and ½ teaspoon almond extract. Attach the dough hook and mix on low speed until the ingredients are combined.
• With the mixer on low, add 2½ cups of the all-purpose flour. Continue mixing until the dough begins to form.
• If the dough is still very sticky, add additional flour 1 tablespoon at a time, up to a total of 3 cups, until the dough pulls away from the sides of the bowl. The dough should be somewhat tacky but not sticky.
• Knead the dough on low in the mixer until it is smooth and cohesive. Stop the mixer, shape the dough into a ball, and transfer it to a lightly greased bowl.
• Cover the bowl tightly with plastic wrap and place it in a draft-free, warm spot. Allow the dough to rise until roughly doubled in size, about 2 hours.
• Gently press the center of the risen dough to deflate it. Wrap the dough tightly in plastic wrap and refrigerate for 6 to 8 hours or overnight.
• Remove the chilled dough. On a lightly floured surface, roll the dough to about ½ inch thickness. Use a donut cutter (or a large round cutter and a 1-inch cutter for the hole) to cut out donuts and donut holes. Re-roll scraps as needed.
• Place the cut donuts and donut holes on a parchment-lined baking sheet. Lightly cover with plastic wrap, then drape a clean dry towel over the top. Let them rest at room temperature for up to 1 hour (do not exceed 1 hour).
• In a large Dutch oven (or deep heavy pot), pour vegetable oil to a depth of 2 to 3 inches and heat over medium until the oil reaches 350°F. Use a thermometer to monitor temperature; avoid overheating the oil.
• Fry the donuts in batches so the pot is not overcrowded. Carefully lower donuts into the hot oil and fry until golden brown on the first side, then flip and fry until golden brown on the second side. Remove cooked donuts with a slotted spoon and place them on a baking sheet fitted with paper towels and a cooling rack. Repeat until all donuts are fried.
• In a separate mixing bowl, whisk together the powdered sugar, milk, 1 teaspoon vanilla extract, and ½ teaspoon butter extract (optional) until smooth and lump-free.
• When the donuts are slightly cooled but still warm to the touch, dip each donut into the glaze, flip to coat both sides, and return to the cooling rack set over the baking sheet to catch drips. Allow the glaze to set for about 10 minutes before serving.