Place a rack in middle of oven; preheat to 350°. Toss beets, garlic, chile powder, oregano, paprika, cumin, pepper, 1 Tbsp. Diamond Crystal or 1½ tsp. Morton kosher salt, and ⅓ cup oil in a medium bowl until beets are coated. Scrape onto a foil-lined rimmed baking sheet; bake, tossing every 15 minutes, until beets are tender and spices are very fragrant and smell slightly toasted, 35–45 minutes.

Meanwhile, heat 2 cups oil in a large saucepan over high until oil bubbles immediately when the edge of a tortilla touches the surface. Carefully fry onion, adding a little bit at time to avoid too much spattering and reducing heat as needed, until tender and beginning to brown, about 5 minutes. Transfer to a paper-towel-lined baking sheet. Repeat process with chiles, about 5 minutes. Transfer to same baking sheet. Fry sage leaves until crisp, about 30 seconds. Transfer to baking sheet. Working one at a time, fry tortillas, turning once, until crisp, puffed in places, and deep golden brown, about 1 minute per side. Transfer tostadas to baking sheet.

Heat remaining oil in a large nonstick skillet over medium-high. Fry crumbled tofu until starting to brown, about 4 minutes. Season with black salt, smoked paprika, turmeric and nutritional yeast.

Spoon beet mixture onto tostadas, dividing evenly, and top each with tofu scramble, then fried onion, chiles, sage, and Salsa de Árbol.