Heat olive oil in a large skillet over medium-high heat. Add diced chicken and sprinkle with chili powder, cumin, paprika, garlic powder, onion powder, salt, and pepper. Cook for 6-8 minutes, stirring occasionally, until cooked through.

In a small bowl, combine Greek yogurt, nutritional yeast, hot sauce, apple cider vinegar, and salt. Stir until smooth.

Warm the large tortillas to make them pliable. Lay one flat and spoon a quarter of the chicken and sauce mixture into the center. Sprinkle with cheese.

Place a tostada shell on top of the chicken. Spread a thin layer of the remaining sauce, then top with shredded lettuce and diced tomatoes.

Fold the edges of the large tortilla towards the center, creating pleats until the filling is fully enclosed.

Place the wrap seam-side down in a lightly oiled skillet over medium heat. Cook for 2-3 minutes per side, until golden brown and crispy. Repeat for the remaining wraps.