Bake the mozzarella sticks according to the package instructions.
Meanwhile, start the grilled cheese. Heat a griddle or large skillet over medium-low heat. Butter 1 side of each slice of bread and arrange the slices buttered-side down on the griddle. Top each slice of bread with 3 slices of cheese and cover with a lid to help the cheese melt. Cook until the bottom of the bread is toasted and golden brown and the cheese is melted, 4 to 5 minutes.
Top 2 of the bread slices with 3 baked mozzarella sticks each. Top with the remaining bread slices to form 2 sandwiches. Slice and serve.