Drizzle the olive oil and Balsamic vinegar over the tomatoes and season with salt and pepper.
Grill the tomatoes until they start to burn and char. Remove from the heat and allow to cool in a dish while you make the dressing.
To make the dressing, combine all the ingredients in a blender or food processor (you can use a hand-held blender too or just chop everything finely by hand) and blend until smooth.
To assemble, tear the mozzarella and place on a large plate. Top with the grilled tomatoes, drizzling their resting juices over the cheese and tomatoes. Drizzle the basil dressing over the salad and add fresh basil leaves then serve.