Trim the pork of fat and set two large 3 to 4 inch pieces of white pork fat aside to use later. Cut pork into 1 inch cubes. Place flour, salt, and black pepper in a bag and mix well. Add the cubes of pork. Shake the pork cubes in the flour mixture until meat is well covered.
Heat olive oil over medium-high heat in large stockpot. Add chopped onions and garlic and cook for 10 minutes, stirring frequently, but be sure to allow onion to brown slightly.
NOTE: Try cooking pork in batches. All at once ended up with black char layer on the bottom of the pot.
Add dredged pork cubes, the reserved two pieces of pork fat and stir with onion and garlic. Allow the pork to brown, cooking for up to 15 to 20 minutes, stirring frequently, until pork cubes are seared on all sides and bottom of pan has nice amount of brown bits from the pork and onion.
Remove cooked large pieces of fat and discard.
Add chicken stock, green chile (about 1 1/4 to 1 1/2 cups of chopped chile) and chopped canned tomatoes. With a wooden spoon, gently scrape bottom and sides of pan to help flavor the stock. With no lid on the stockpot, allow chile to come to a boil and then reduce heat to a light simmer. Simmer for 1 to 1 1/2 hours, or until pork is tender. Salt to taste. The green chile should be rich and brown in color.
Just before serving add fresh cilantro to chili.