Pat pork chops dry, then sprinkle on both sides with 1 teaspoon salt and 1/2 teaspoon pepper (total).
Heat oil in a 12-inch heavy skillet over medium heat until it shimmers, then cook pork chops, turning once, until browned and just cooked through, 10 to 12 minutes total. Transfer to a platter and keep warm, loosely covered with foil. Pour off all but 1 tablespoon fat from skillet.
Heat butter in skillet over medium heat until foam subsides, then cook shallots with thyme, stirring occasionally, until tender and golden-brown, about 5 minutes.
Add 1/4 cup brandy to skillet and carefully ignite with a kitchen match (use caution; flames will shoot up), then cook over medium heat, scraping bottom of skillet to loosen brown bits. When flames subside, add peaches, preserves, and 1/4 teaspoon each of salt and pepper and cook, covered, until peaches are tender and juicy, about 3 minutes. Stir in remaining tablespoon brandy, any meat juices from platter, and salt and pepper to taste, then spoon sauce over chops.