1. 1. Activate the yeast: In a large bowl, combine warm milk, active dry yeast, and 1 tablespoon of the granulated sugar. Stir gently and let sit for 5-10 minutes until foamy.

2. 2. Prepare dough base: To the yeast mixture, add eggs, melted butter, remaining ½ cup granulated sugar, and salt. Whisk until smooth.

3. 3. Combine wet and dry: Gradually add flour, starting with 3 cups, mixing with a wooden spoon or dough hook. Add more flour a little at a time until a shaggy dough forms that pulls away from the bowl.

4. 4. Knead: Turn dough onto a lightly floured surface. Knead for 8-10 minutes (or 6-8 minutes in a stand mixer with dough hook) until smooth, elastic, and slightly tacky.

5. 5. First rise: Place dough in a lightly oiled bowl, turn to coat. Cover with plastic wrap or a towel. Let rise in a warm, draft-free place for 1 to 1.5 hours until doubled in size.

6. 6. Shape: Punch down dough. Roll to ½-inch thickness and cut into 3-inch rounds, or divide into 12-16 equal pieces and shape into balls. Place on parchment-lined baking sheets, spaced apart.

7. 7. Second rise: Cover loosely with plastic wrap or towel. Let rise for 30-45 minutes until puffy.

8. 8. Heat oil: In a large heavy pot, heat 6-8 cups vegetable oil to 350-360°F. Use a deep-fry thermometer.

9. 9. Fry: Carefully lower 2-3 bomboloni into hot oil. Fry 2-3 minutes per side until golden brown. Do not overcrowd.

10. 10. Drain and coat: Remove with a slotted spoon. Transfer to a wire rack over paper towels to drain. While warm, roll in the reserved ½ cup granulated sugar or dust with powdered sugar.

11. 11. Fill: Once slightly cooled, use a piping bag with a long thin nozzle to inject filling into the side of each bomboloni until plump.