Lightly crush the fennel seed in a mortar and pestle or with the bottom of a small skillet. Transfer to a small bowl and stir in 2 tsp. salt and 1/4 tsp. pepper. Season the pork chops with 3 tsp. of the spice mixture.
Melt the butter over medium heat in a 12-inch skillet. Stir in the fresh fennel, 1/2 cup of the broth, and the remaining spice mixture. Cover the skillet, increase the heat to medium high, and cook, stirring occasionally, until the fennel begins to soften and brown, 8 to 10 minutes (reduce the heat if the fennel browns too quickly).
Uncover, reduce the heat to medium, and add the remaining 1/4 cup broth and 2 Tbs. of the parsley. Cook, stirring frequently and scraping up any browned bits, until tender, 1 to 2 minutes. Stir in the remaining parsley and the fronds, season to taste with salt and pepper, and transfer to a medium bowl.
Wipe out the pan, add the oil, and heat over medium-high heat. Add the pork chops and cook, turning once with tongs, until well browned and cooked through, 10 to 12 minutes. (To check for doneness, make a small cut near the bone and look inside.the pork should still have a hint of pinkness.) Serve the pork chops with the fennel.