Preheat the oven to 350 degrees F (175 degrees C).

Melt butter in a large skillet over medium heat. Add garlic, and sauté until fragrant. Season pork chops with salt and pepper, then fry them in the skillet just until browned on both sides, about 3 minutes per side. Remove pork chops to a baking pan or Dutch oven.

Pour mushrooms into the skillet with the pork drippings and garlic, and stir in the sherry and beef broth, scraping up any bits of pork that are stuck to the pan.

Bring to a boil, then pour over the pork chops in the baking pan. Cover with a lid, or aluminum foil.

Bake for 45 minutes in the preheated oven, then remove the lid or foil, and continue to bake for another 15 minutes.

Remove chops from the pan to a serving platter, and place the baking pan on the stovetop over medium heat. Stir together cornstarch and water. When the juices in the pan come to a boil, slowly stir in cornstarch mixture and cook until thickened, about 2 minutes. Spoon sauce over chops, and serve.