In a large bowl, whisk together the warm milk, yeast, and sugar. Let sit for 5–10 minutes until foamy.
Add the egg and melted butter.
Gradually mix in flour and salt until a soft dough forms.
Before all the flour is all incorporated, add in the chopped dried tomatoes and grated parmesan cheese.
Knead for about 8-10 minutes until smooth and elastic. The dough should be soft but not overly sticky.
Place dough in a lightly greased bowl, cover, and let rise in a warm place for 1 to 1½ hours or until doubled in size.
Punch down the dough and divide into 12 equal pieces.
Tuck the corners into the middle to start to form a ball. With the smooth side facing up, form roll into tighter ball by cupping the palm of your hand and gently rolling and pressing into the table.
Place rolls seam-side down in a greased 9x13 baking dish.
Cover loosely and let rise in a warm place for another 30 minutes until puffy.
Preheat oven to 350℉.
Bake rolls for 18-20 minutes or until golden brown on top.
Mix together melted butter, garlic, and parsley.
Brush over warm rolls immediately after baking and sprinkle with grated parmesan if desired.