Microwave the baby spinach for 30 seconds at a time until the spinach has wilted.
For each sandwich: squeeze a tablespoon of mayonnaise (about a tablespoon) over a slice of bread. Top the bread with a slice of cheese, 4 slices of ham, half of the baby spinach, and a tomato slice. Add a slice of cheese on top and cover a slice of bread.
Place the sandwiches in a pan or skillet and cook over medium heat for about 3-5 minutes per side, until the bread is toasted and the cheese has melted.