Combine 1/2 cup flour and pepper in a shallow bowl or dish. Place panko in a second shallow bowl or dish. Combine 1/2 cup half-and-half and egg in a third shallow bowl or dish; stir with a whisk.
Sprinkle both sides of pork chops with salt. Dredge 1 pork chop in flour mixture. Dip in egg mixture; dredge in breadcrumb mixture. Repeat procedure with remaining pork chops, flour mixture, egg mixture, and breadcrumb mixture. Cover and chill 15 minutes.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat until hot. Add chops to pan; cook 2 minutes or until lightly browned. Remove chops from pan; add remaining 1 tablespoon oil to pan. Turn chops over; return to pan. Cook 2 minutes or until lightly browned. Remove from pan; keep warm.
Heat butter in pan over medium-high heat. Add onion; sauté 1 minute. Add mushrooms; sauté 3 minutes. Add garlic; sauté 1 minute. Add wine to pan; cook until liquid almost evaporates, scraping pan to loosen browned bits. Combine 1/2 teaspoon flour and 1 teaspoon water in a small bowl; stir with a whisk. Add to cooking liquid in pan. Bring to a boil; cook 1 minute, stirring constantly. Add stock; bring to a boil. Cook until reduced to 1 1/4 cups (about 6 minutes). Stir in 1/2 cup half-and-half. Cook 3 minutes or until thick, stirring constantly. Remove from heat; stir in parsley and chives. Serve sauce with pork chops.