For preparation, put the green chilies, jalapeños, and diced tomatoes in a blender or food processor container. Puree until you get a homogenous mixture. Set the puree aside.
Put 2 tbsp. of butter and the cooking oil in a pot large enough to hold all the ingredients. Heat on a medium setting on the stove.
When the butter melts, add the pork. Occasionally stirring, cook until the meat is light brown.
Add the onions and sauté for a few minutes until they become soft and translucent.
Add the tomato paste, spices, salt, and garlic. Cook for two minutes.
Pour the chili-tomato mixture into the pot. Add 2 cups of beef stock and 1 cup of water.
Reduce the heat to very low. Cover the lid and simmer for about an hour.
Start preparing the roux during the last ten minutes of cooking. Put the remaining butter in a medium-sized saucepan. On a low heat setting, melt the butter. When the butter melts, add the flour. Stirring constantly, cook for about 2 minutes or until the butter separates from the flour.
Add small quantities of the remaining beef stock and water using a ladle. Stir continuously until the roux thickens. Remove the saucepan from the heat when it has a thick but pourable consistency.
Add the roux to the green chili pot. Mix until the dish is well blended. Cover the lid, and let the mixture simmer on very low heat for about 10 minutes.
Transfer the chili onto a serving platter or divide it into individual plates. Garnish with green onions and lemon wedges.