Preheat the oven to 425 degrees F.
Toss the sweet potatoes in a medium bowl with 1 tablespoon oil, cumin and 1/4 teaspoon salt. Spread on a baking sheet and roast until soft and partially browned, 25 to 30 minutes.
Spray both sides of the tortillas with cooking spray, then stack them up and cut the stack into 8 triangular pieces. Separate the tortilla pieces and lay them out onto a baking sheet. Sprinkle with the chili powder and 1/4 teaspoon salt and toss. Bake the chips until crisp, about 15 minutes, tossing the chips halfway through the baking time. Remove the chips from the oven and toss them with the lime zest.
Heat 2 teaspoons of the oil in a medium skillet over medium-high heat. Add half of the onions and cook, stirring, until soft, about 4 minutes. Add the adobo sauce and tomato paste and stir until the tomato paste darkens slightly, about 2 minutes. Add the beans and 3/4 cup of water and simmer the sauce until it thickens and the beans are heated through, about 5 minutes. Set aside until ready to assemble the nachos.
Combine the tomatoes, remaining onions, serrano chile, lime juice, remaining 1 teaspoon oil and 1/4 teaspoon salt in a food processor. Pulse until the mixture becomes a chunky salsa.
To assemble the nachos, mound half of the tortilla chips in a 9-by-13-inch baking dish. Scatter most of the beans and the sweet potatoes over the chips. Sprinkle with half of the cheese. Mound the rest of the chips over the cheese and finish with the remaining beans, sweet potatoes and cheese. Place in the oven until the cheese melts, 5 to 7 minutes. Top with the avocado, salsa and cilantro.
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