Preheat the oven to 350 degrees F (175 degrees C). Coat a baking sheet with nonstick spray.

Place tofu slices onto a plate and place another plate on top. Set a 3- to 5-pound weight on top. Press tofu for 20 to 30 minutes; drain and discard the accumulated liquid. Cut each slice into 1-inch cubes.

Mix vinaigrette, egg white, Parmesan cheese, lemon juice, and balsamic vinegar together in a large bowl. Fold tofu gently into the marinade and let sit for 5 to 10 minutes.

Arrange marinated tofu in a single layer onto the prepared baking sheet, reserving marinade.

Bake in the preheated oven for 25 minutes. Turn tofu and drizzle with remaining marinade. Bake until just browned, about 10 minutes more.

Combine mushrooms, mango, baby spinach, and red onion in a large salad bowl. Arrange a serving of salad on a plate; place a portion of baked tofu on top. Repeat with remaining salad and tofu.