Carefully trim off any excess fat from the pork and cut it into bite-sized pieces. Set aside for later use.

In a large pot, heat up a tablespoon of lard over medium heat until shimmering. Add in the finely chopped onions and cook until they become translucent, for about 5 minutes. Then add in the minced garlic and allow it to cook for an additional minute.

Once fragrant, remove the onions and garlic from the pot and set them aside. In the same pot, heat up another tablespoon of lard over medium-high heat until hot. Working in batches, add half of the pork pieces to the pot and cook them until they are evenly browned on all sides, for about 5 minutes. Using a slotted spoon, remove the pork from the pot and transfer it onto a plate. Repeat this step with the remaining pork.

Now, add in the green chilies, tomato paste, diced tomatoes, canned jalapeños, chicken broth, water, black pepper, dried oregano, ground cumin, and dried sage to the pot with lard. Stir well until everything is fully combined.

Increase the heat to high and bring the chili to a boil. Once boiling, reduce the heat to low and add back in the browned pork pieces. Give it a good stir and let it simmer for about an hour, partially covered with a lid.

Meanwhile, in a separate saucepan, melt a cup of lard over medium heat until hot and bubbly. Gradually add in the flour while constantly stirring until you get a smooth paste-like consistency.

Slowly pour this roux into the chili while continuously stirring to incorporate it well. Let the chili simmer for an additional 30 minutes until it thickens to your liking.

Once done, turn off the heat and serve the chili in bowls, topped with your choice of toppings such as shredded cheese, dollop of sour cream, or sliced avocado. Pair this hearty and flavorful chili with some warm tortillas or freshly baked cornbread on the side.