Make compote: Combine ingredients in a 2- to 3-quart saucepan; bring to a simmer, cover and cook until fruit is soft but not falling apart, 30 minutes. Remove and discard cinnamon stick. (Compote can be made and refrigerated up to 4 days ahead. Reheat, adding up to 1 cup water to loosen.)
Cook pork: Heat a large cast-iron skillet over medium heat. Season pork chops with salt and pepper and add to pan. Cook until browned on bottom, about 6 minutes. Turn and cover pan loosely; cook about 6 minutes more, until meat is firm to the touch. Transfer chops to a board, tent loosely with foil and let stand for 5 minutes.
Arrange chops on plates and spoon compote on top.