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Preheat oven to 325 degrees. In a small bowl, whisk together red wine, chicken stock, and tomato paste. Set aside.
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Heat a large Dutch oven over medium-high heat. Season the brisket all over with 3/4 tsp. salt and 1/4 tsp. black pepper, Coat pan with cooking spray. Add brisket to pan and brown on all sides, approx. 8 minutes total. Make sure the meat is nicely brown as the brown bits on the bottom of the pan will flavor the onions and gravy.
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Remove brisket from pan, cover meat and set aside. Add 1/2 tsp. salt, 1/4 tsp. pepper, sliced onions, sugar, and thyme to pan. Cook for 20 minutes or until the onions are tender and golden brown. Stir occasionally, scraping up the brown bits on the bottom of the pan.
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Add garlic, carrots, and celery and cook for 5 minutes, stirring occasionally. Place brisket on top of onion mixture and pour wine over the meat. Cover the pot and place in the oven. Bake at 325 degrees for 1 3/4 hours.
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Remove pot from oven. Turn meat over, cover pot and return to oven. Cook for another 45 minutes or until beef is tender. You might need another 15 minutes or so. Remove from oven; cover and keep warm.
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Remove brisket from pan and cut across the grain into thin slices. Serve with onions and gravy. Sprinkle with chopped fresh parsley.