Heat extra virgin olive oil in a large soup pot or Dutch oven over medium-high heat. Add sweet potatoes, poblano peppers, and shallots, season with salt and pepper, then saute until sweet potatoes begin to soften, 5 minutes. Add chorizo then saute until cooked through, breaking it up as it cooks. Add garlic then saute for 30 seconds.
Add remaining ingredients then stir to combine and turn heat up to bring to a boil. Turn heat down to medium-low then place a lid partially on top and simmer until sweet potatoes are tender, 10-15 minutes, stirring occasionally and scraping off any fat from the chorizo that rises to the top. Taste then adjust seasoning if necessary, and then serve with toppings.