Salt and pepper, to tastePeel the avocados and remove the seeds from the center. Slice the avocados into long, thin strips. Slice the tomatoes into thin slices as well. Slice the cheese if it is not already. Heat a panini griddle or a flat griddle and turn to medium heat. Assemble the sandwiches with some mayo and pesto on both sides of the bread (mayo is optional). Spread the pesto mixture. Place a slice of cheese on both sides of the inside of the bread/sandwich. Slice the tomatoes and avocados on top of one slice of bread. If you like fresh basil, place some basil leaves on the top of the avocados. If you are using turkey, you can add several slices to the sandwich at this point. Place the sandwich lid onto the sandwich after seasoning with salt and pepper. Spread a thin layer of butter onto each side of the sandwich and place on the griddle. Heat the sandwich until nicely golden brown on both sides and the cheese is melted. Serve sandwiches warm or cold.
Notes
HEALTHIER OPTION: Omit the mayonnaise to cut calories. Use less pesto than is called for. Use one slice of cheese instead of two and serve on whole wheat bread.