How to Make It
Preheat oven to 400°F. Toss sweet potato and poblanos with cumin, 1 tablespoon oil, and ½ teaspoon salt in a bowl; spread in a single layer on a rimmed baking sheet. Roast until vegetables are tender, about 25 minutes, stirring halfway through.
Meanwhile, whisk lime juice and remaining 3 tablespoons oil and ¼ teaspoon salt in a large bowl. Add cabbage, radishes, and cilantro and toss to coat.
Spread refried black beans on tostadas. Top with sweet potato mixture, slaw, and sour cream; serve with lime wedges.