In a small bowl, combine the warm milk, yeast and about a teaspoon of the sugar. Set aside in a warm spot and let sit until foamy and frothy, about 10 minutes.
In the bowl of a stand mixer, fitted with the dough hook, combine the flour, milk mixture, sugar, salt, eggs and butter and mix on medium until it comes together. Knead on high for about 8 to 10 minutes, until smooth and somewhat soft. Transfer the dough to a well-oiled bowl and cover with plastic wrap and a damp kitchen towel. Let rest in a warm spot until doubled in size, about 1½ hours.
Punch dough down and then transfer the dough to a lightly floured work surface. Roll out into a large rectangle about ¼-inch thick. Spread evenly with the softened butter, and sprinkle with the chopped garlic, parmesan, paprika and parsley. Roll into a tight long, length wise, and then cut into 12 even pieces. Place on a well greased 9 by 13-inch baking pan. Cover loosely with plastic wrap and a damp kitchen towel. Allow to rest in a warm spot until doubled in size, about 1 hour.
Preheat oven to 350°F.
Bake the rolls until puffed and golden brown, about 30 to 35 minutes. Remove from the oven and let cool slightly.
Meanwhile, to make the topping, melt the butter in a small saucepan, set over low heat. Add the garlic and parsley and cook until the garlic has softened, stirring often, about 5 minutes. Brush over the warm buns and serve. Enjoy!