Heat 1 1/2 tablespoons oil in a medium saucepan over medium-high heat. Add onion and pepper and cook, stirring occasionally, until tender, 4 to 6 minutes. Add chili powder and cook, stirring, until fragrant, 30 seconds. Add black beans and 1/3 cup water. Reduce heat to medium-low and cook, stirring occasionally, until thickened, 4 to 6 minutes. Mash beans with the back of the spoon until thick. Stir in lime juice. Season with salt and pepper.
Meanwhile, toss carrots with cumin and 1 1/2 tablespoons oil on a rimmed baking sheet. Season with salt and pepper. Roast, turning once, until just tender, 10 to 12 minutes.
Divide beans and carrots between taco shells. Top with avocado, queso fresco, cilantro, and radishes. Serve with lime wedges alongside.