01 - Dissolve sugar in warm milk in a small bowl. Sprinkle yeast over the surface, stir gently, and let stand for 5 to 10 minutes until foamy and activated.
02 - Combine flour and salt in a large bowl. Add melted butter, egg, and the activated yeast mixture. Stir until a shaggy dough begins to form.
03 - Turn dough onto a lightly floured surface and knead for 8 to 10 minutes until smooth and elastic. Transfer to a greased bowl, cover, and let rise in a warm area for approximately 1 hour until doubled in size.
04 - While dough rises, combine softened butter, minced garlic, parsley, salt, and Parmesan in a small bowl. Mix until thoroughly incorporated and spreadable.
05 - Punch down the risen dough to release air. Divide into 12 equal portions. Flatten each piece into a small rectangle, spread with 1 to 2 teaspoons garlic butter, roll tightly, and pinch seams to seal.
06 - Place rolls seam-side down in a greased 9x13-inch baking pan. Cover loosely and let rise for 20 to 30 minutes until puffy and expanded.
07 - Preheat oven to 350°F. Brush risen rolls with melted butter and sprinkle with parsley and additional Parmesan if desired.
08 - Bake for 20 to 25 minutes until rolls are golden brown and cooked through. Serve warm for optimal flavor and texture.