These sandwiches were cooked on a grill, but a skillet would work just as well. Choose your favorite kind of cheese. We prefer a variety that melts easily, such as Gouda or Swiss, but cheddar is also good.
Butter one side of each slice of bread. Arrange 4 slices, buttered side down, on clean work surface. Divide cheese evenly among 4 slices of bread. Arrange tomato slices over cheese, cutting slices in half to fit if necessary. Scatter basil leaves over tomatoes. Top with remaining slices of bread, buttered side up.
Place sandwiches on a medium-hot grill, off direct heat. Cook until bread is golden and cheese is beginning to melt, about 4 minutes depending on heat of grill.
Turn sandwiches over, and continue grilling until bread is golden and cheese is completely melted. Move to a slightly cooler part of the grill to melt if bread is darkening too much.