If you have a wide, flat-bottomed soup pot, use that; otherwise, set a large, deep-sided skillet over medium heat (you'll need a soup pot later). Add oil to 1/4-inch depth and let oil get hot enough that a bit of tortilla sizzles when added. Working carefully in batches, fry tortillas about 1-minute per side, just until golden. Using tongs, remove cooked tortillas to a paper towel-lined plate. If needed, edge heat down slightly as you fry.

After cooking the tortillas, add the completely dry chilies to the hot oil for one minute. Things may spit and pop, so have a lid handy. Set fried chilies on a paper towel to cool.

Let oil cool for a minute, then carefully pour off all but 1/4 cup. If already using a soup pot, set that back over medium heat. If not, heat a soup pot over medium heat and then add the hot 1/4 cup of oil. Add onions and cook, stirring often. When cool enough to handle, remove stem and seeds from chilies, rough chop, and stir into the pot along with salt and pepper. After 8 minutes total, add the garlic. Working quickly, add the tomatoes and 4 cups broth. Bring mixture to a boil. Crumble in half the tortillas, and turn soup down to a gentle simmer. Cook 15 minutes, stirring occasionally.

Using an immersion blender or working in batches with a blender, blend the soup (don't overdo it – the soup should still have some texture). Return soup to cooking pot, and gently reheat. Cover with a lid if soup bubbles and spits. If needed, add up to 1 cup more broth (or water) to thin the soup. Add salt and pepper to taste.