01 - Dissolve sugar in warm milk in a small bowl. Sprinkle yeast over the surface, stir gently, and let stand for 5–10 minutes until mixture becomes foamy and activated.
02 - Combine flour and salt in a large mixing bowl. Add melted butter, egg, and activated yeast mixture. Stir until shaggy dough begins to form and pulls away from sides of bowl.
03 - Turn dough onto lightly floured surface and knead for 8–10 minutes until smooth and elastic. Transfer to greased bowl, cover with damp towel, and let rise in warm draft-free area until doubled in volume, approximately 1 hour.
04 - While dough rises, combine softened butter, minced garlic, parsley, salt, and Parmesan in small bowl. Mix thoroughly until uniform and spreadable consistency is achieved.
05 - Punch down risen dough to release air. Divide into 12 equal portions. Flatten each piece into small rectangle, spread with 1–2 tsp garlic butter mixture, roll tightly from short end, and pinch seam firmly to seal.
06 - Place rolls seam-side down in greased 9x13-inch baking pan. Cover loosely and let rise for 20–30 minutes until puffy and increased in size by about half.
07 - Preheat oven to 350°F. Brush risen rolls generously with melted butter. Sprinkle chopped parsley and additional Parmesan evenly over surface.
08 - Bake for 20–25 minutes until rolls are deeply golden brown and sound hollow when tapped lightly. Transfer to wire rack and serve warm for optimal texture and flavor.