Combine milk and sugar in a stand mixer with a hook attachment. Add yeast and allow to sit, 10 minutes. Add salt, butter, egg, and garlic, and mix together. Add flour ½ cup at a time.
Knead on medium speed, 5-7 minutes. Dough should pull away from the bowl. Transfer to a lightly greased bowl and cover with plastic wrap and a damp towel. Let rise, 1 hour.
Whip Boursin cheese, butter, and salt together. Punch the dough down. Transfer to a floured work surface. Roll out to a ¼-inch thick rectangle. Spread the cheese mixture evenly over the dough and sprinkle with parmesan.
Roll lengthwise and cut into 1-inch pieces. Place in a well-greased, 7 inch skillet. Cover with plastic wrap and a damp towel and place in a warm place for 1 hour.
Preheat oven to 350 degrees F. Brush tops with melted butter and sprinkle with parmesan. Bake swirls for 30-35 minutes or until golden brown. Brush again with melted butter, top with parsley, and sprinkle with salt.