Preheat griddle to low. Place a saucepan on the griddle.
Assemble the sandwich: Slice the Cuban bread down the middle and lay it flat. Spread mayo and mustard on both sides of the bread.
Layer the smoked turkey, ham, and cheese on the bread.
In the saucepan on the griddle, combine butter and minced garlic. Stir until well mixed. Pour some of the butter-garlic mixture onto the griddle and place the sandwich on top. Use the griddle press on the sandwich.
While the sandwich is cooking, finely chop lettuce, tomatoes, and onions.
Flip the sandwich and add more butter and garlic to the other side.
Remove the sandwich from the griddle. Open the top of the Cuban bread and add the chopped veggies. Close it back up, slice, and enjoy!
