Place two pieces of bread, butter side down on a plate or cutting board.
Layer two slices of cheese, turkey slices, pesto, 1 or 2 slices of tomato, and two slices of cheese onto the bread. Top with the slice of bread, butter side up. Repeat for each sandwich.
Heat a pan over medium high heat. Place one or more sandwiches on the pan and press down with the weight.
Cook 1 to 2 minutes or until grill lines become clearly defined.
Flip and cook the sandwich for 1 to 2 more minutes or until grill lines become clearly defined. Serve hot from the panini pan.