Add pork chops to the brine, cover, and refrigerate for at least 4 and up to 8 hours. When ready to cook, remove pork, pat dry and discard brine.
Season pork liberally with Cajun seasoning and salt and let come to room temperature. Grill (or cook in an oiled skillet over mediumhigh heat) until it reaches an internal temperature of 140°F on a meat thermometer. Remove to a plate, tent with foil, and let sit for 5 to 10 minutes before serving.
While pork rests, heat a small skillet over medium heat, then add rye, Cognac, and bitters (be very careful on a gas stove, as the liquor will flame). Cook until liquid reduces to 2 to 3 tablespoons, about 4 minutes. Remove from heat and whisk in butter one piece at a time; return pan briefly to the heat only if the butter stops melting. Taste and add salt, if needed.
Pour sauce over the pork chops, garnish with fennel fronds, and serve immediately. Serves 4.
