Preheat the grill to medium.
Cut the tomato in half and grate it on the coarse side of a box grater. Reserve the tomato pulp.
Grill the bread slices on both sides until they are slightly charred. When the bread comes off the grill rub each slice with a garlic clove and drizzle generously with olive oil. Top each toast with tomato pulp and a tiny sprinkle of salt. Cover tomato with a slice of ham and serve.