Preheat oven to 450°. Heat oil in a large ovenproof frying pan over medium-high heat. Rub pork chops with 1/2 tsp. salt and 1/2 tsp. pepper and cook until golden brown on one side, about 3 minutes. While pork cooks, core and roughly chop escarole. Transfer pork to a plate.
Add 2 tbsp. broth, the vinegar, brown sugar, and remaining 1/4 tsp. each salt and pepper to pan and simmer 1 minute. Add shallots, squash, sage, and escarole to pan. Cook until escarole has wilted, about 5 minutes, mixing occasionally with tongs.
Put frying pan in oven and bake, uncovered, until squash is just tender, about 20 minutes. Remove from oven and fit pork, browned side up, between vegetables. Drizzle remaining broth over mixture and sprinkle walnuts on top. Return to oven and bake, uncovered, until vegetables begin to turn golden and pork is cooked through, 5 to 10 minutes.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.