Grease a medium bowl with oil or nonstick spray. Line a baking sheet with parchment paper and lightly flour it. Line a wire rack with paper towels. Set all aside.
Combine the warm water, milk, sugar, and yeast in a large bowl. Whisk to dissolve the yeast. Allow the yeast to proof for about 5 minutes or until it starts to foam.
7 cups water, 2 tablespoons milk, 3 tablespoons granulated sugar, ¼ ounce fast-acting dry yeast
Add the remaining donut ingredients to the bowl with the yeast mixture. Stir to combine. Transfer the mixture to a stand mixer fitted with the dough hook or to a clean work surface to knead by hand. Knead on low speed (or by hand) for about 5 minutes, or until the dough is nice and smooth.
3¾ cups all-purpose flour, 1 large egg, 6 tablespoons unsalted butter, ⅓ teaspoon baking powder, ½ teaspoon kosher salt
Place the dough into the greased bowl, cover with plastic wrap, and let rise in a warm, draft-free place until almost doubled in size, about 1 hour.
Punch the dough down and roll out on a lightly floured surface to ½-inch thick. Use a 3-inch cutter to cut the donuts. Place the donuts onto the prepared baking sheet, cover with plastic wrap, and let proof for 15 minutes. Re-roll the remaining dough, cut out the remaining donuts and add them to the baking sheet.
Heat 2 inches of oil in a Dutch oven to 350-360°F. Drop 2-3 donuts at a time and fry until golden, about 2 minutes per side.
Remove the donuts from the oil and place on the prepared paper towel-covered wire rack. Let cool before filling.