Cozy up a cold night with this elevated comfort food dish.
Let the chops rest a bit at room temperature to take the chill off.
Preheat a large cast-iron skillet over medium-high.
Pat the chops dry with paper towels; season with salt, white pepper, and 1 tsp. brown sugar. Drizzle the chops with about 2 tbsp. oil. Add the chops to the skillet; cook until browned, 4 to 5 minutes per side. (If they have a fat cap along the edges, pick up the chops with tongs and brown the fat.) Transfer the chops to a plate.
Reduce heat to medium. Add the remaining 2 tbsp. oil, two turns of the pan, to the skillet. Add the shallots and rosemary and cook, stirring often, until the shallots soften, 1 to 2 minutes. Stir in the garlic, then the vinegar, caper berries, butter, and the remaining 2 tbsp. brown sugar. Slide the chops back into the skillet. Reduce heat to low and simmer, turning the chops often, until the chops are cooked through, 8 to 10 minutes.
Meanwhile, in a medium saucepan, bring the stock and milk just to a boil over medium-high. Whisk in the polenta, then whisk until thickened, about 3 minutes. Stir in the Parmesan and the butter; season the polenta.
Divide the chops among plates. Top with the sauce. Serve the greens and polenta alongside.