Prepare the Aromatics: Heat 3 tablespoons of olive oil in a large sauté pan over medium heat. Add the finely diced onions and minced garlic, cooking until the onions become soft and translucent, about 5 minutes. Stir frequently to prevent burning.
Cook the Sweet Potatoes with Spices: Add the grated sweet potatoes to the pan along with chili powder, cumin, and cayenne pepper. Reduce heat to low and cover the pan. Let the mixture cook gently for 8 to 10 minutes, stirring every few minutes to keep it from sticking or burning. The sweet potatoes should become tender and flavorful.
Season and Finish Filling: Season the cooked sweet potatoes with salt and black pepper to your liking. Remove the pan from heat. Stir in the chopped cilantro and squeeze fresh lime juice over the mixture. Taste and adjust seasoning with additional lime juice or salt as needed.
Warm Tortillas and Beans: While the filling is cooling slightly, warm your tortillas in a dry skillet over medium heat for about 30 seconds each until pliable. Warm the black beans in a small skillet or microwave until heated through.
Assemble the Burritos: Lay a warm tortilla flat on a plate. Layer with a leaf or two of lettuce, followed by a scoop of black beans, a sprinkle of cheese, a generous spoonful of the sweet potato filling, and a dollop of sour cream. Finish with a squeeze of fresh lime juice.
Roll and Serve: Fold in the sides of the tortilla, then roll it up tightly from the bottom to enclose all the fillings. Slice each burrito in half and serve immediately with extra lime wedges on the side.