In a large resealable plastic bag, combine flour, 2 tablespoons ancho powder or Essence, and Kosher salt and shake to mix well. Add 1 pork shank at a time and shake to coat. Place pork shanks on a platter or a baking sheet once they have been coated.
In a heavy Dutch oven or cast-iron skillet, heat 2 tablespoons vegetable oil over medium-high heat. When hot, add pork shanks in batches and brown all sides, about 10 minutes. Transfer browned shanks to a roasting pan (we used a 2 gallon roasting pan, just large enough to hold the shanks in one layer) and set aside.
Preheat oven to 325 degrees.
Add remaining 2 tablespoons oil to Dutch oven along with onion, pepper, celery, and garlic and cook over medium low heat until vegetables are wilted and onion is translucent. Add sauteed vegetables to roasting pan. Transfer roasting pan to the cooktop and add 1 tablespoon Essence, bay leaves, oregano, and stock and bring to a boil. Cover roasting pan with aluminum foil and place in oven for 2 1/2 to 3 hours, or until meat is fall-from-the-bone tender. Check periodically to make sure that shanks remain submerged in liquid. Transfer braised shanks to a large, deep platter, cover, and keep warm. (The recipe can be made up to this point up to several days in advance and refrigerated. Rewarm gently if preparing in advance.)
Strain cooking liquid, pressing on the solids; discard solids. Skim any fat from surface and cool broth, reserving for another use.
Preheat the oven to 475 degrees.
Place pork shanks on a rack resting on a baking sheet lined with aluminum foil. Brush all sides of shanks with Spicy New Mexican Barbecue Sauce. Place shanks in oven to brown, about 15 minutes. Remove shanks from oven and spoon more barbecue sauce over meat. Serve barbecued pork shanks with Cheddar Jalapeno Cornbread and a simple cole slaw (if desired). Make sure to have lots of napkins handy.
Cook's Note: Once the shanks are cooked, the meat becomes extremely tender and will literally fall off the bone. If you would like to serve the whole shank in one piece, you must be very careful when plating. If you prefer, the meat can be pulled from the bone and then served like pulled pork.