For the green chili: Cook the pork in some vegetable oil
in a heavy-bottomed pot or Dutch oven
over medium heat until the meat is browned on the outside and a little pink on the interior. Add the garlic and onion and cook until soft. Add the flour and stir until brown. Add some water (up to 1 cup) and adjust according to the desired thickness. Add the chicken broth and stir to combine. Add the canned tomatoes and chiles, roasted green chiles, serrano chiles
, cumin, cilantro, cayenne, salt, black pepper and white pepper
and bring to a boil. Turn the heat to low and simmer
uncovered, stirring constantly, for 2 to 3 hours. If you need to thicken the chili, add more flour. If you need to thin it, add more broth.
For the burgers: Mix the beef, cayenne and salt and pepper to taste. Shape into 8 patties Prepare a grill or grill pan to medium-high heat. Grill the burgers to desired doneness.
To serve: Grill the buns until grill marks show. Place the bottom of 1 bun in a bowl. Top with 1 burger, some Monterey Jack, Cheddar and green chili. Add the top of the bun and more green chili, Monterey Jack and Cheddar. Sprinkle with some onions. Serve with a knife and fork. Reserve the remaining chili for another use.