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. Stir in salt and pepper to taste.

Slice each tomato along its equator; then gently remove seeds (so sandwiches don’t get soggy). 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, making four sandwiches. Halve before serving.