Slice the steak into thin strips: Cut the steak into thin strips against the grain.
Make the marinade: Whisk together 1/3 cup olive oil, soy sauce, vinegar, sugar, cumin, and minced garlic in a large bowl.
Marinade the steak: Place the sliced steak in the marinade and coat thoroughly. Cover in plastic wrap and marinate for 30 minutes to 1 hour (If you marinate it longer, place it in the fridge).
Make carne asada: Heat 1 tablespoon of oil in a large skillet over medium-high heat. Once hot, take the steak from the marinade (discard the liquid), and add to the skillet. Stir-fry for about 5 minutes until cooked through. (If there is too much liquid during cooking, you can scoop it out.)
Assemble mulitas: Brush the tortillas with oil on both sides. Place one tortilla in the skillet, sprinkle cheese evenly on top, and then add about a layer of carne asada, and sliced onions. Add more cheese, and then place a tortilla on top. Cook the bottom until golden brown for about 1-2 minutes, and then carefully turn to the opposite side and continue to cook until golden brown. Remove the cooked mulita to a plate.
Add toppings: Gently peel the top tortilla and add mashed avocado, diced tomatoes, and cilantro. Repeat the process with the remaining tortillas, cheese, and the filling. Serve warm with your favorite toppings.