Heat oven to 400 degrees. Lay bread slices on a rimmed baking sheet. Brush both sides with olive oil. Toast for 8 to 10 minutes, until lightly golden brown. Rub each piece of bread with the cut side of a garlic clove.
Grate tomatoes on the large holes of a grater; discard the skins. Season with salt. Spoon 1 teaspoon tomato over each piece of bread. Arrange a small slice of ham over the tomato, and serve immediately.