Heat the oven to 200°F (100°C). Slice the tomatoes, and arrange them on a baking sheet. Sprinkle with salt, a little sugar, the garlic, and thyme. Drizzle with olive oil and bake for about an hour. Meanwhile, bring a medium pot of water to a boil. Dip the basil in the water and then plunge into ice water. Puree the basil leaves in a blender with the 3 1/2 tbsp. (50 ml) olive oil. Slice the mozzarella and season lightly with salt and pepper. Make the stacks by layering the mozzarella and semi-candied tomato slices. Drizzle with olive oil and garnish with the basil sauce.
9 oz. (250 g) buffalo mozzarella 3 1/2 tbsp. (52 ml) extravirgin olive oil; more for drizzling 4 ripe tomatoes 1/2 oz. (15 g) fresh basil, or about 30 leaves sugar garlic, finely sliced fresh thyme salt and pepper