Grease a grill press or grill pan with vegetable oil.
Put four slices of bread on a work surface, put on top of a few spinach leaves, on them slices of tomatoes, sprinkle with 1/8 teaspoon of salt and 1/8 teaspoon of pepper. Top with onion and basil, sprinkle with cheese and add the remaining spinach leaves. Cover with the remaining bread slices and press down well.
Place the tomato and cheese sandwiches on the grill, cover and cook for about 2-3 minutes. If you are grilling sandwiches in a grill pan, press them down well with something heavy, and then turn the tomato and cheese sandwiches on the other side and fry as well.