Season pork chops on all sides with 1/2 teaspoon salt, and 1/2 teaspoon pepper; set aside. Combine the flour, 1/2 teaspoon salt, 1/2 teaspoon pepper, nutmeg, and allspice in a plastic bag. Toss pork with seasoned flour to coat, and shake off excess.
Heat butter and olive oil in a skillet over medium-high heat until lightly smoking. Sear pork until golden brown on each side, about 3 minutes per side. Pour in apple cider and bring to a boil. Turn heat to medium-low, cover, and simmer until pork is fork tender, 15 to 20 minutes. Remove pork and keep warm.
Increase heat to medium-high. Dissolve cornstarch in the chicken broth, and stir into simmering cider; cook for a minute or two until thickened. Stir in the half-and-half and simmer until hot. Serve sauce over the pork chops.