Heat a large skillet over medium-low heat and add the butter. Add in the onion, garlic paste, ginger, garlic, salt and pepper. Cook until softened, about 5 minutes.

Add in the ground pork or chicken, breaking it apart with a wooden spoon. Brown the meat, stirring often, for about 6 minutes. Stir in the hoisin sauce, soy sauce, tomatoes and lime juice. Bring the mixture to a boil then reduce it to a simmer and cook until the mixture thickens, about 20 minutes.

Serve the sloppy joes on the brioche buns, topped with both the broccoli slaw and napa cabbage.