Preheat the oven to 325 degrees F.
In a shallow 9 by 9-inch baking dish, add the flour, salt, pepper, and paprika. Mix well. Dredge each pork shank into the flour until evenly coated. Shake off excess flour.
In a large heavy casserole dish or Dutch oven over medium-high heat, add the grapeseed oil. Sear the shanks on all sides until evenly browned, about 5 to 7 minutes. Remove the seared shanks to a platter. Add onions, celery, carrots, garlic, rosemary and thyme to the Dutch oven. Cook stirring frequently until vegetables soften, about 3 to 4 minutes. Add the sherry and allow the wine to reduce by half. Stir in the chicken broth and beef stock. Bring to a boil and add the shanks back to pan. Cover and put into the oven. Braise until the meat is fork tender and pulling away from the bones, about 2 to 2 1/2 hours. Turn oven off. Remove the shanks from the pot and arrange on a quarter sheet tray, cover with foil and keep warm in the oven. Skim off any excess fat and strain liquid into a large mixing bowl, discarding the solids. Put the strained liquid back into the braising pot and bring to a simmer over low heat.
Sift the flour, salt, garlic powder and pepper into a medium-sized mixing bowl. Combine the butter into flour with your hands until well incorporated. Add the chives and the soup. Mix together well with your hands to form a soft dumpling dough. Drop the dumpling dough by the tablespoonfuls into the strained liquid with an additional 1 cup of chicken stock. Cook the dumplings for 8 to 10 minutes. Arrange the pork shanks on a platter and ladle the sauce and dumplings over top.