Stir together 1/4 cup apple juice, 1 Tbsp. brown sugar, and mustard in a large zip-top plastic freezer bag; add pork. Seal bag, and shake well to coat. Chill 30 minutes, turning once. Remove pork from marinade, discarding marinade. Pat pork dry, and sprinkle with 1/2 tsp. salt and 1/2 tsp. pepper.
Cook pork in hot oil in large skillet over medium-high heat 3 minutes on each side. Remove chops from skillet.
Cook onion and garlic in hot drippings, stirring constantly, 1 minute. Add remaining 3/4 cup apple juice to skillet, stirring to loosen particles from bottom of skillet. Stir in rosemary, 1 Tbsp. brown sugar, 1 Tbsp. balsamic vinegar, and remaining 1/2 tsp. salt and pepper.
Bring onion mixture to a boil. Reduce heat to medium low, and simmer 3 to 5 minutes or until mixture is reduced by half.
Add pork to onion mixture, turning to coat. Cover and cook 5 to 10 minutes or until a meat thermometer inserted in thickest portion registers 155°. Remove from heat, and place pork on a serving platter. Cover with aluminum foil. Let stand 5 minutes.
Meanwhile, whisk together 1/4 cup water, 1 Tbsp. flour, remaining 1 1/2 Tbsp. brown sugar, and remaining 1 Tbsp. balsamic vinegar in skillet until smooth. Bring to a boil over medium-low heat. Reduce heat to low, and simmer 1 to 2 minutes or until slightly thickened and bubbly. Drizzle sauce over pork, or serve with pork, if desired. Garnish, if desired.
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Subbed local honey for the brown sugar and it was delicious! Also thickened the sauce with potato starch instead of flour since I can't eat flour. Served it with some sauted green beans with leeks and sliced rosemary/garlic bread - the husband loved it!
I've made this twice now and it's now one of my favorite pork chop recipes. Only thing I did differently is I used italian seasoning with rosemary in it along with basil and oregano. I think that much rosemary on its own would be a bit overwhelming. I served it with brussel sprouts sauteed with a little bit of the balsamic sauce and my family loves it.