Directions

1. Stir together scallions, jalapeño, radishes, lime juice, fine sea salt, and vinegar in a small bowl. Let stand, uncovered, at room temperature while preparing tostadas, stirring occasionally to ensure vegetables are evenly marinated.
2. Preheat oven to 350°F. Place beets in a 13- x 9-inch baking pan. Add 8 garlic cloves, lime quarters, guajillo chile pieces, 1/4 cup kosher salt, 2 teaspoons cumin, coriander, and crushed red pepper, if using. Drizzle beets with 2 tablespoons oil; add just enough water to come halfway up sides of beets. Place a piece of parchment paper over beets, and cover pan tightly with aluminum foil.
3. Roast beets in preheated oven until just fork-tender, 1 hour to 1 hour and 30 minutes. Remove from oven, and let stand, covered, 15 minutes. Drain beets, and let cool completely, about 30 minutes. Discard braising mixture. Peel beets; grate using the large holes of a box grater. Set grated beets aside, covered, at room temperature.
4. While beets braise, heat remaining 2 tablespoons oil in a small saucepan over medium. Add onion, remaining 2 garlic cloves, and remaining 1 teaspoon kosher salt; cook, stirring often, until onions are translucent and softened, 4 to 5 minutes. Stir in chile powder and remaining 1 teaspoon cumin; cook, stirring constantly, until fragrant, about 30 seconds. Add black beans and their liquid; cook, stirring often, until heated through, 4 to 5 minutes. Transfer mixture to a blender. Add lime juice, and process until smooth, about 30 seconds. Set aside.
5. Arrange tostada shells on a flat surface. Spread about 2 tablespoons black bean puree in an even layer on each tostada shell. Sprinkle reserved grated beets with flaky sea salt, and toss to combine. Scatter about 1/4 cup grated beets on each tostada. Drain reserved pickled vegetables, and divide evenly among tostadas; top evenly with queso fresco and pepitas. Garnish with cilantro; serve with lime wedges.