Thaw the spinach, then squeeze out as much water as possible. You should have about 1 cup chopped spinach before squeezing the water out and about 1/2 cup after squeezing.
Drain the artichoke hearts well, then chop them into small bite-sized pieces. Add the chopped artichokes to a large bowl with the spinach, mozzarella, Parmesan, mayonnaise, garlic powder, crushed red pepper, salt, and pepper. Stir the ingredients until evenly combined.
Spread about 1/2 tsp butter on each slice of bread. Pack about 1 cup of the cheese and vegetable mixture between two slices of bread, buttered sides facing out.
Place the sandwiches in a large skillet and cook over medium-low heat until the outsides are golden brown and the filling has melted. Serve immediately.