Put 1 tablespoon lemon juice and next nine ingredients (chickpeas through salt) in a food processor. Pulse until finely chopped, but not puréed. Form chickpea mixture into three 3/4-inch-thick patties, pressing firmly to compress so they don’t crumble.

Heat a skillet over medium heat; then add olive oil. Cook patties 5 minutes. Flip and cook for 4–5 more minutes, until a sharp knife inserted into a patty’s center feels hot to the touch.

While patties cook, dice cucumber. Combine remaining 1 tablespoon lemon juice, cucumber, and feta in a small bowl.

Remove cooked patties to serving plates. Top with cucumber-feta salad and serve immediately.