Heat the oven to 400 degrees.
Prepare your tofu: Drain it, squeezing out any excess moisture over the sink. Coarsely grate the drained tofu onto two large (11-by-17-inch), foil-lined sheet pans. Drizzle the tofu in each pan with 2 tablespoons olive oil and 1 tablespoon soy sauce. In a small bowl, mix the cumin, paprika, garlic powder, onion powder, cayenne, 1 teaspoon salt and 1 teaspoon pepper; sprinkle half the seasonings over each pan and toss to coat. Spread the mixture in an even layer.
Roast the tofu, stirring halfway through and rotating the pans, until the tofu sizzles, darkens and crisps, 30 to 35 minutes.
In a small bowl, mix together the tomato paste with the remaining 3 tablespoons oil. Drizzle the mixture over the tofu, adding half to each pan, then toss to combine, spread into an even layer and roast again until the tofu audibly crackles and develops a slight crunch, 10 to 15 minutes.
While the tofu roasts, prepare the avocado cream: In a small food processor (or blender), blend the avocados, mayo, lime zest and juice until creamy; season generously with salt.
Swipe the warmed tortillas with the avocado cream, then top with tofu mixture, red onion, radishes and cilantro. Serve immediately.
