Wash the tuna and cut into very fine cubes. Peel garlic and shallots, cut into very fine cubes and add half each to the tuna. Add 2 teaspoons of oil, season to taste with 1 teaspoon of lime juice, salt and pepper. Cut 5 chives into very fine rings and add half to the tartar. For the salsa, wash, clean, quarter and seed the tomatoes. Cut the flesh into small cubes. Mix remaining garlic and shallots cubes with 1 teaspoon of oil, remaining lime juice and chive rolls.
Add tomato cubes, except for 1 teaspoon, to the salsa. Peel the lime so that the white skin is completely removed. Remove the fillets with a sharp knife between the parting skins and add to the salsa, except for a few for garnishing. Season to taste with salt and pepper. Serve the tartar on pumpernickel. Garnish with diced tomatoes, lime fillets and chives. Pour the salsa into a bowl and serve with the pumpernickel snacks