Halve the avocado, remove the pit, and dice the flesh. Peel the mango and carefully slice the flesh off the seed. Dice half the mango. Chop half the cilantro. Halve the lime. In a medium bowl, combine the diced avocado, diced mango, chopped cilantro, and juice from half the lime. Add a pinch of salt and stir the mango avocado salsa to combine.
Trim, deseed, and halve the jalapeño. In a blender, combine half the jalapeño, remaining mango, remaining cilantro, 1 clove garlic, juice from the remaining lime half, 1 tbsp olive oil, and 1 tbsp water. Blend until smooth, taste, and season with salt.
Drain and rinse the black beans. Mince the remaining 2 cloves garlic. Mince the remaining jalapeños. Place a large nonstick skillet over medium heat with 2 tsp olive oil. Add the minced garlic, minced jalapeño, and cumin and cook until fragrant, about 1 minute. Add the black beans, ½ cup water, and ¼ tsp salt. Mash half of the beans with the back of a fork and cook until the beans have thickened, about 2 to 3 minutes.
Transfer the mashed black beans to a bowl. Rinse, dry, and return the skillet to medium-high heat with 1 tbsp olive oil. Add 3 corn tortillas in a single layer. Spoon 2 tbsp of the black beans onto half of each tortilla and fold in half. Cook until crispy, about 1 minute per side, then transfer to a plate. Repeat with the remaining tortillas. Sprinkle the crispy tortillas with a pinch of the chili powder and salt.
In a medium bowl, toss the red cabbage with half the cilantro sauce and a pinch of salt. Open the tacos gently, and fill with red cabbage and mango avocado salsa.
Serve the crispy black bean tacos with the remaining cilantro sauce. Dollop with half the sour cream (reserving the other half for the Italian Stuffed Zucchini recipe).