Prepare a wood or charcoal fire in a grill with a cover.

Thread a skewer across and down the rib flaps of the rabbit to close the cavity. In a small bowl, combine the mustard, garlic, olive oil, tarragon, parsley, salt and pepper to make a paste. Using a spatula, spread the paste all over the rabbit.

When the coals are hot, push them to the sides of the fire pan and place a large drip pan in the bottom of the grill. Oil the grill rack and place the rabbit on it, directly over the drip pan. Grill uncovered for 15 minutes, then cover the grill, leaving both the bottom and top air vents open, and grill the rabbit for 15 minutes longer.

Remove the lid and, if necessary, add more coals to maintain the heat at 375–400° F. Turn the rabbit over and replace the cover. Continue to cook until the meat is opaque throughout the thickest part of the leg and saddle, about another 30 minutes.

Transfer the rabbit to a cutting board. Using kitchen shears or a knife, cut the rabbit into serving pieces. Arrange on a warmed platter and serve hot.