Activate yeast: In a small bowl, stir warm water and sugar; sprinkle yeast on top. Let foam for 5–7 minutes.
Mix dough: In a large bowl or stand mixer, whisk flour and salt. Add yeast mixture, warm milk, and melted butter.
Knead: Knead on medium speed (or by hand on a floured surface) until smooth and elastic, about 6–8 minutes.
First rise: Place dough in a lightly oiled bowl, cover, and let rise until doubled, 1–1½ hours.
Prep filling: Cube cheeses and pat dry.
Shape bombs: Punch down dough. Divide into 12–16 pieces (~2 oz each). Flatten each into a disk, place a cheese cube inside, pinch edges to seal, and roll into a ball.
Second rise: Arrange on parchment‑lined sheets, cover, and let puff for 20–30 minutes.
Make garlic butter: Melt butter over low heat, add garlic, cook 1–2 minutes. Remove from heat, stir in parsley, salt, and pepper.
Bake: Preheat oven to 375 °F (190 °C). Brush bombs with garlic butter. Bake 15–18 minutes until golden.
Finish: Immediately brush again with remaining garlic butter and sprinkle Parmesan and extra parsley.