Cut a round of parchment paper that fits inside of a large cast iron skillet.
Pat dry pork chops and generously season with salt and pepper. Preheat cast iron skillet over high heat. When smoking, add oil and swirl to coat. Add pork chops in an even layer. If necessary, cook in batches so as not to overcrowd pan. Place prepared parchment round on top of chops and top with additional skillet or two to encourage searing. Cook, flipping once, until golden on the edges, about 2-2 1/2 minutes per side. Replenish oil if necessary between batches.
Remove pork chops to a plate. Add thyme sprigs, honey mustard, and chicken broth. Cook until reduced by half. Add butter and capers and swirl to emulsify. Season with lemon juice, salt, and pepper and pour sauce over pork chops.
Add 2 tablespoons olive oil and garlic to skillet. Cook, stirring, until garlic is sizzling and begins to turn golden, about 1-2 minutes. Add mustard greens, toss to coat, and season with salt and pepper. Cook just until wilted, about 30 seconds. Remove from heat.
Serve pork chops with mustard greens, additional fresh thyme, and red pepper flakes, if desired.