In the bowl of a mixer, stir 1 envelope yeast into 1/2 cup plus 2 tablespoons warm water. Let stand until foamy, 5 minutes. Add 1 cup flour. Beat on low speed until well combined. Cover, and refrigerate overnight. Bring to room temperature.
In another bowl, combine remaining 1 envelope yeast, 2 tablespoons warm water, and buttermilk. Let stand until foamy, 5 minutes. Combine sugar, salt, and remaining 2 1/4 cups flour in the bowl of a mixer. Add buttermilk mixture, egg yolks, and butter. Beat on low speed until dough comes together, about 2 minutes.
Add flour-yeast mixture. Beat until dough is soft and sticky, 3 to 4 minutes. On a floured surface, knead dough a few turns into a ball. Place dough, smooth side up, in a bowl coated with cooking spray. Cover, and let stand in a warm place until doubled in bulk, 3 to 4 hours.
Divide dough into thirds, and cover with plastic wrap. Roll each piece to 1/4 inch thickness on a floured surface. Using a 1 1/2-inch round cutter, cut out doughnuts; using the 1/2-inch round end of a pastry tip, cut out centers. Place on a parchment-lined baking sheet. Let stand in a warm place for 15 minutes.
Fill a saucepan halfway with oil and heat to 350 degrees. Fry doughnuts, turning once, until golden brown, about 1 minute. Drain on paper towels. Coat with sugar while warm, and serve immediately.
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