Heat oven to 350°F. Line a 9x13-inch pan with parchment for easy cleanup.
Beat cream cheese until smooth. Mix in sour cream and mayonnaise until creamy.
Stir in spinach, artichokes, mozzarella, 1/2 cup Parmesan, garlic, Worcestershire, lemon juice, onion powder, red pepper, salt, and pepper.
Slice the rolls horizontally. Set the bottoms in the pan, cut-side up.
Spread the spinach-artichoke mixture evenly over the roll bottoms.
Place the roll tops on. Mix melted butter with garlic powder and parsley, then brush over the tops.
Sprinkle the tops with the extra Parmesan. Cover the pan tightly with foil.
Bake 15 minutes. Uncover and bake 8–10 minutes more, until the cheese is melty and tops are golden.
Rest 5 minutes. Slice along the seams and serve warm.