Peel the sweet potato and cut it into small, even cubes. Dice the onion and mince the garlic. Drain and rinse the beans, and measure your spices so cooking moves smoothly.
Warm the olive oil in a large pot over medium heat. Add the diced onion and cook for 3 to 4 minutes. Stir now and then until it turns soft and translucent.
Stir in the garlic and sweet potato. Cook for about 2 more minutes, stirring often. The garlic will smell amazing, and the sweet potato will get a light coating of oil.
Sprinkle in the chili powder, cumin, smoked paprika, and salt. Stir until every piece of vegetable looks evenly coated. Give it about a minute so the spices can warm up and release their aroma.
Add the diced tomatoes with their juices, then the rinsed black beans and the broth or water. Stir well, scraping the bottom of the pot. Bring it to a gentle bubble.
Let the chili simmer uncovered for 20 to 25 minutes, stirring occasionally. The sweet potato should turn tender and the sauce should thicken. If it gets too thick, stir in a small splash of broth.
Press a few sweet potato pieces against the pot with the back of a spoon for a thicker texture. Let the chili rest for a bit, or chill it overnight if you can wait. Ladle it into bowls and add your favorite toppings.