Preparation Stir together yeast and milk in bowl of mixer and let stand until foamy, about 5 minutes. (If mixture doesn't foam, start over with new yeast.) Mix in 3/4 cup flour. Cover bowl with plastic wrap and a kitchen towel and let dough rise in a draft-free place at warm room temperature until doubled and bubbly, about 1 hour. Mix in egg, butter, sugar, salt, and remaining 1/2 cup flour at low speed until combined. Increase speed to medium and beat dough until satiny and elastic, 5 to 7 minutes. Scrape dough into center of bowl and dust lightly with flour. Cover bowl with plastic wrap and a kitchen towel and let dough rise at warm room temperature until doubled, about 1 hour. Line a baking sheet with wax paper and lightly sprinkle with flour. Punch down dough and turn out onto a lightly floured surface. Cut into 16 equal pieces. With lightly floured hands, flatten 1 piece of dough and put a cheese cube in center. Pinch closed, then roll into a ball and transfer to baking sheet. Make 15 more balls, arranging 1 inch apart. Heat 2 inches oil in a 2-quart heavy saucepan over medium heat to 350°F. Fry bomboloni, 4 at a time, turning frequently, until puffed and golden, about 2 minutes per batch. Transfer with a slotted spoon to paper towels to drain. Return oil to 350°F between batches. Serve hot. Cooks' note:• Bomboloni can be filled and formed (but not fried) 1 day ahead and chilled, covered.
Preparation Stir together yeast and milk in bowl of mixer and let stand until foamy, about 5 minutes. (If mixture doesn't foam, start over with new yeast.) Mix in 3/4 cup flour. Cover bowl with plastic wrap and a kitchen towel and let dough rise in a draft-free place at warm room temperature until doubled and bubbly, about 1 hour. Mix in egg, butter, sugar, salt, and remaining 1/2 cup flour at low speed until combined. Increase speed to medium and beat dough until satiny and elastic, 5 to 7 minutes. Scrape dough into center of bowl and dust lightly with flour. Cover bowl with plastic wrap and a kitchen towel and let dough rise at warm room temperature until doubled, about 1 hour. Line a baking sheet with wax paper and lightly sprinkle with flour. Punch down dough and turn out onto a lightly floured surface. Cut into 16 equal pieces. With lightly floured hands, flatten 1 piece of dough and put a cheese cube in center. Pinch closed, then roll into a ball and transfer to baking sheet. Make 15 more balls, arranging 1 inch apart. Heat 2 inches oil in a 2-quart heavy saucepan over medium heat to 350°F. Fry bomboloni, 4 at a time, turning frequently, until puffed and golden, about 2 minutes per batch. Transfer with a slotted spoon to paper towels to drain. Return oil to 350°F between batches. Serve hot. Cooks' note:• Bomboloni can be filled and formed (but not fried) 1 day ahead and chilled, covered.