Season the pigeon breasts generously on both sides. Return the frying pan to the heat with the remaining olive oil. Once the oil is sizzling hot, add the pigeon breasts, skin side down. Press the skin down into the pan if it curls up slightly. Cook the breasts for 3 minutes, before turning over and cooking for a further 2 minutes on the other side. Place on a board to rest for 3 minutes while assembling the rest of the salad.