Combine chickpeas, paprika, cumin, coriander, caraway, garlic, lemon juice, and olive oil in a food processor. PULSE a few times until chickpeas are coarsely chopped and slightly pasty, but not smooth. Season with salt and pepper to taste.
Cut tomatoes into 1/4-inch slices.
Spread each bread slice with chickpea mixture. Top half of the slices with tomatoes, then basil, feta, and grated carrot. Top with remaining bread slices. Cut in half before serving.