Take 2 tomatoes from the tin and cut them into cubes. Mash the rest of the tomatoes in the juice. Peel onion and garlic. Finely dice onion, press garlic through a garlic press.
Heat the fat in a pot, fry the onions and garlic until transparent. Add tomato puree and stock and season with salt and pepper. Bring to the boil and simmer for about 5 minutes. In the meantime, wash the basil, dab dry and cut into fine strips, except for a little garnish.
Cut the ham into strips as well. Add the diced tomatoes and half of the basil to the hot soup and season again. Divide into soup bowls and sprinkle some ham into each soup.
Serve sprinkled with a dash of crème-fraîche and remaining basil and pepper.