Peel and cube sweet potatoes into 3/4-inch pieces, dice the onion and bell peppers, mince the garlic and chipotle pepper, and drain and rinse both cans of beans. Open all canned goods and measure out the broth before you begin cooking.
Heat olive oil in a large Dutch oven over medium heat, then add the diced onion and cook for 5 to 6 minutes until soft and translucent. Add the minced garlic and cook for 1 to 2 minutes, then stir in the bell peppers and cook for 3 to 4 minutes more until slightly softened.
Push the vegetables to the center of the pot to create a well, then add all the spices (chili powder, cumin, smoked paprika, coriander, oregano, and cayenne) directly to the hot surface. Stir constantly for 60 seconds until fragrant, then mix in the chipotle pepper and adobo sauce until everything is well coated.
Add the cubed sweet potatoes and stir to coat them in the spiced vegetable mixture. Pour in the fire-roasted crushed tomatoes, diced tomatoes, vegetable broth, salt, and black pepper, and stir everything together.
Bring the chili to a full boil over medium-high heat, then reduce to a gentle simmer over low heat with the lid slightly askew. Cook for 20 to 25 minutes, stirring every 5 to 6 minutes, until the sweet potatoes are completely fork-tender.
Stir in the drained black beans and kidney beans and simmer for 5 to 8 minutes more. For a thicker consistency, pulse the pot 3 to 4 times with an immersion blender or mash 1 cup of the chili separately and stir it back in.
Squeeze the juice of 1 lime into the pot and stir to combine. Taste the chili and adjust with additional salt, cayenne, or lime juice as needed.
Ladle the hot chili into bowls and top with freshly chopped cilantro. Add your choice of optional toppings such as sour cream, shredded cheese, sliced avocado, pickled red onions, or tortilla chips.