"This is what is known in New Mexico as a 'bowl of green.' The heat depends on how hot your chiles are, and fresh late-summer Hatch chiles are the best ingredients. It is easily made with or without meat, and the vegan version loses nothing in terms of flavor. Serve with tortillas. It also freezes and reheats well."
Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil. Place Hatch chile peppers, cut sides-down, onto the prepared baking sheet.
Cook peppers under the preheated broiler until the skin has blackened and blistered, 6 to 8 minutes. Place blackened peppers into a bowl and tightly seal with plastic wrap. Allow peppers to steam as they cool, about 20 minutes. Discard skins and chop peppers.
Heat oil in a soup pot over medium heat. Add onion and garlic; cook and stir until softened, about 5 minutes. Add chiles; cook and stir until fragrant, 3 to 5 minutes. Pour in chicken stock; mix briefly. Sift in flour, whisking well until no lumps remain. Bring mixture to a boil. Reduce heat to low and simmer soup until flavors combine, about 20 minutes.
Blend soup in the pot using an immersion blender. Season with salt and pepper.
Substitute chicken stock with vegetable stock for a vegan version.
If you don't have an immersion blender, puree the soup in a blender, being careful of the hot liquid. If you like more than a 'bowl of green,' then you can add potatoes, pork or chicken, or other vegetables after you blend it. Let them simmer about 15 minutes in the cooked dish to absorb the flavors.