De-stem (and optionally deseed) the mulato chiles. In a pan, toast the mulato chiles on each side (10-30 seconds) until fragrant. Toast the round chiles until fragrant. Put toasted dried chiles into a heatproof bowl, cover with hot or boiling water, and let stand for 10-30 minutes. (See section on rehydrating chiles for more info and shortcut options.)
In a blender or food processor, blend the rehydrated chiles along with their soaking water together with the fresh Thai red chiles (de-stemed) and optionally, a handful of the chopped sweet peppers. Add more water if the consistency is too thick. You should end up with a smooth, pourable puree. If using tortilla to thicken the chili, blend at this step (see note ***).
Heat oil in a large pot over medium heat and sauté the onions until translucent. Add oregano and cumin and fry until fragrant (10-30 seconds).
Add the remaining ingredients to the pot. Add the can of diced tomatoes, chili puree, and chopped sweet potato and sweet peppers. Rinse the cans of beans and add to the pot. Also add the masa or corn flour, if using, at this step (see note ***).
If the ingredients are not already submerged, add enough water to cover. Stir and bring to a boil. Then simmer, stirring occasionally, over low-medium heat for 20-30 minutes, or until sweet potatoes are cooked.
Season with salt to taste. Serve with avocado, cilantro, or other garnishes.