Peel the tomatoes (optional, for a smoother texture): score them with a cross, blanch in boiling water for 30 seconds, then place in ice water. Remove the skin.
Dice them finely and place in a bowl.
Add the olive oil, walnut oil, salt, pepper, and finely chopped basil. Mix and let marinate for 5 to 10 minutes at room temperature. Toast the bread slices in the oven or a pan until golden and crispy.
Rub the bread immediately with a halved garlic clove.
Spoon the marinated tomato mixture over the toasted bread.
Top each slice with pieces of burrata and a slice of cured ham.
Finish with a drizzle of olive oil or a few drops of walnut oil.