- Preheat oven to 300 degrees. Mix creole spice, paprika, salt, and mustard together. Place pork shoulder in large roasting dish and season with half dried spice mixture. Pour chicken stock into dish and add thyme, bay leaves, half each of the diced onion and peppers, and the diced tomatoes. Cover with foil and bake for 8 hours, or until pork is fork tender.
- Remove pork from oven and cool in refrigerator. Strain braising liquid through a fine mesh strainer and skim away any fat that comes to surface. Set aside.
- To a large saucepan over medium heat, add bacon. Slowly render bacon until all fat is released, about 8 minutes. Add remaining vegetables, garlic, and cumin to pan. While stirring with a wooden spoon, cook down vegetables until they're falling apart. Add tomato paste and flour and continue to cook until all fat and vegetables are absorbed by flour. Whisk braising liquid into vegetables slowly to prevent lumps. Cook for about 1 hour, skimming away any fat that rises to surface. Strain through fine mesh sieve into saucepan and place over low heat to keep warm.
- Remove pork from fridge, cut into 2-inch chunks, and add to sauce. Once pork has heated through, serve over grits.
In a medium saucepan over medium heat, warm milk until it scalds. (Milk is scalded when skin forms on top and it begins to bubble around the edges.) Whisk grits into milk and lower heat to medium-low. Cook for 10 minutes, whisking occasionally to prevent clumps. Finish by whisking in butter, heavy cream, salt, and pepper. Cover, remove from heat, and reserve until needed.