Here is the gist:
Season your chops with salt and pepper and cook them with indirect heat. We built a fire in the middle of our fire pit grill and cooked the chops on the ring grill until they were almost cooked through, about 120ºF.
After stoking the fire with some new splits of wood, we added the center grate and heated the cast iron griddle on top of that. It only takes a few moments to sear the outside of the chops on that hot iron.
With the chops seared, we add butter and oil to the pan, fry the sage leaves for a moment, pour in the blackberries, stir, and then deglaze with a pour of water. I add salt, sugar, and vinegar to taste. If the pan is extra hot the sugar goes in right at the end to avoid burning. There is enough water in the pan to boil the blackberries and break them down. More water can always be added to extent the cooking. When the sauce is reduced to a consistency you like, quickly toss the chops in it and pour the rest of the sauce on top. The chops will be well rested at that point and ready to serve.