For the pesto basil, wash, shake dry, pluck off the leaves and set aside about 1⁄4. Peel and chop the garlic. Grate parmesan. Finely puree the rest of the basil, garlic, parmesan, almonds and 5 tbsp. oil in a tall beaker with a hand blender.
Season with salt and pepper.
Dab mozzarella dry and cut into slices. Finely dice the tomatoes. Peel shallots and cut into slices. Peel, wash and chop carrots.
Heat the butter in a pot. Saute the shallots and carrots over a low to medium heat for 7-8 minutes while turning. Season with salt and pepper.
In the meantime, place slices of bread next to each other on the work surface. Spread with the pesto. Divide the mozzarella into 4 slices, leaving a rim of about 1 cm free. Cover with the pesto bread slices and press the sides together firmly with your fingers.
Heat 2 tablespoons of olive oil in portions in a large or two smaller pans. Carefully place the sandwiches in the pan and fry until golden on each side. Fold the rest of the basil under the carrots and shallots.
Serve with mozzarella sandwiches. Sprinkle with tomatoes.