For the crostini with tuna tartare, squeeze the limes and mix the juice with the chili sauce in a bowl. Cut the tuna into small cubes (5 x 5 mm), mix with the marinade and marinate covered in the refrigerator for about 1 hour.
In the meantime, toast the sesame seeds in a pan without oil until golden brown. Wash the cilantro and shake dry. Pluck the leaves from the stems. Set aside a few leaves, chop the rest as finely as possible. Cut the bread into 15 slices. Heat 3 tablespoons olive oil in a large skillet and toast the bread slices until golden brown on both sides, drain on paper towels.
Remove the tuna from the refrigerator. Fold in the sesame seeds, chopped cilantro and 2 tablespoons olive oil. Season the spread with salt and pepper, spread the tuna tartar on the toasted bread slices and arrange with the remaining coriander leaves. Serve the crostini with tuna tartare.