Preheat broiler. Season pork with 1/2 tsp. salt and the pepper; set aside.
Heat 2 tbsp. oil in a large frying pan over medium heat. Add shallots and cook, stirring often, until caramelized, 7 to 8 minutes. Transfer shallots to a small bowl. Add 2 tbsp. oil to pan and increase heat to medium-high. Add greens and cook until wilted, 2 to 3 minutes. Stir in vinegar, broth, sugar, and remaining 1 tsp. salt. Reduce heat to medium and cook, partially covered, until greens are tender, about 10 minutes.
Meanwhile, mix mustards, jam, and fennel seeds in a small bowl. Heat remaining 2 tbsp. oil in a large ovenproof frying pan over medium-high heat. Sear pork until browned on one side, about 3 minutes. Remove frying pan from heat, turn pork over, and spread mustard mixture over browned side. Broil until pork is just cooked through (145°), 2 to 3 minutes.
Serve pork, mustard side up, with greens on the side. Pour any pan juices over pork chops and garnish pork and greens with shallots.