How to Make It
In a medium frying pan, cook the sausage and onion over moderately high heat, breaking up the meat with a fork, until the sausage is cooked through but not browned, about 4 minutes. Stir in the apple and then pour off the fat. Cool to room temperature.
Put the mustard in a food processor or blender and add the lemon juice, garlic, teriyaki sauce, thyme, lemon zest, pepper and salt. With the motor running, add the oil in a thin stream.
Stuff the quail with the sausage, onion and apple mixture and put them in a large dish. Cover the quail with the mustard sauce and let them marinate for 1 to 2 hours.
Heat the oven to 500°. Lift the quail out of the marinade but let any marinade that clings to the birds remain. Arrange the quail on a rack in a broiling pan, taking care that they don't touch one another, and cook for 7 minutes. Turn the pan and continue cooking until the quail are browned and crisp, about 7 minutes longer. The meat should still be a bit pink.
To serve, spoon the black-eyed-pea relish in the center of six plates and top each serving with two of the quail.