Heat a pan to medium heat and dry toast the dried peppers until they become fragrant, about 30 seconds per side. Remove them from the heat and add them to a pot of boiling water, just enough to cover them.
Turn off the heat and let them rehydrate for 20 minutes.
When the peppers are rehydrated, drain them but reserve a few tablespoons of the darkened water. Remove the stems and seeds from the peppers and add them to a food processor with the reserved water and process to form a paste. Strain, if desired, to remove any remaining bits.
Heat a large pot to medium heat and add the olive oil. Add the potatoes, carrot, peppers and celery and cook, stirring a bit, about 10 minutes to soften everything up.
Add the garlic, chili powder, salt and pepper and stir. Cook another minute.
Add the white wine to deglaze the pan. Stir up the brown bits from the bottom.
Add the chicken stock and swirl in your chili paste. Let it simmer for 20 minutes, though you can easily simer longer to further develop the flavor.
Taste and adjust for salt and pepper.
At this point, you can transfer as much to a food processor and process until smooth. I like to process only about half and leave it a bit chunky. You can also use stick blender.
Swirl in the cheese and stir until it is nicely melted through.
Serve in bowls with fresh herbs, limes, chili flakes and crackers.