Preheat oven to 450F. Place butter in 9x13-inch baking dish. Heat in oven until butter melts. Stir baking mix, milk and sugar in large bowl until soft dough forms. Transfer dough to lightly floured surface. With floured fingertips, pat out dough to 9x13-inch rectangle.
Using sharp knife, cut dough into thirteen 1-inch-wide strips. Cut strips in half crosswise. Place strips evenly atop butter in pan. Sprinkle with Italian seasoning and paprika, then with grated Parmesan. Bake until golden brown, about 20 minutes. Recut strips and serve hot.