Cut diagonal slits through the skin on the pork belly, 1″ apart, then cut intersecting slits at the same spacing so that you create an “X” pattern. Take care not to cut into the fat. This is to allow the rub to penetrate more of the meat.
Cover the pork belly with the Spice Rub.
Heat your smoker to 250 degrees. If your setup includes some kind of liquid pan, add 2 bottles of beer (these are over and above the beer called for in the recipe). Put the pork belly in the smoker, and add the wood of your choice, according to the smoker instructions.
Smoke the pork belly until it reaches an internal temperature of 195 degrees Fahrenheit. Remove from the heat, and allow to rest for 15-20 minutes.
While the pork belly is smoking
Prepare your other ingredients.
Once the pork has completed its rest
Chop the pork belly up into 1/2″ chunks.
In a large pot, add 2 tablespoons of olive oil and heat over medium heat. Once the oil starts to shimmer, add the pork belly. Cook until the fat renders and the pork belly has browned, about 10 minutes.
Increase the heat to medium-high. Add the ground beef and ground pork. Add some salt and pepper, and cook until the meat is cooked through, about 10-15 minutes, stirring every few minutes.
Add the peppers and the onions. Cook for about 10-15 minutes, stirring often, until onions start to become translucent and begin to brown.
Add the garlic. With a spoon, push the ingredients in the pot to the sides to expose the browned bits on the bottom of the pan. Add the beer to deglaze the pot, and use a wooden spoon to scrape up the browned bits off the bottom. Redistribute the ingredients and stir. Cook until the beer has reduced by about half.
Add the chicken stock, tomatoes, and beans. Return to a simmer, and reduce heat to medium low. Allow to simmer for about 20 minutes. Taste along the way, and adjust the seasoning as needed.
Mix the water, masa harina, and chili powder into a thick paste.
When the chili has cooked down, slowly add in the masa harnina paste. This will start tot thicken the chili.
If you desire thicker chili, start adding in the corn starch 1 teaspoon at a time and stirring in, allowing to incorporate. Take your time with this, as if you add too much in, the chili can get too thick.
Cut the tops off of the rolls, and carefully dig out the insides, taking care not to pierce the outside of the crust.
Heat your grill to high. (If you don’t have a grill handy, you can use a broiler with the shelf set to the highest placement.) Place the bread, hole side down, on the grill (or facing up if using the broiler). Toast the roll.
Fill the bread bowls with chili. Add a few pieces of plucked cilantro, and a teaspoon of sour cream. Squeeze a 1/8″ slice of lime onto the chili. Add cheese, if desired.