For the burritos: Heat the oil in a large nonstick skillet over medium-high heat. Add the ground beef and cook, breaking it up, until it is slightly crisp, about 5 minutes. Add taco seasoning packet (without adding the recommended water) and stir untill incorporated. Remove from pan and set aside. Beat the eggs in a medium bowl until frothy. Sprinkle with salt and pepper and a couple dashes of hot sauce. Pour the eggs into the skillet and cook, stirring, until the eggs are fluffy and just set, about 3 minutes. Remove from the skillet and keep warm. Wipe out the skillet and return it to the heat.
Warm the tortillas one at a time in the skillet.
Build the burrito by layering the avocado, egg mixture, beef, onion, and a sprinkle of cheese. Fold in the two sides and roll up tightly. Garnish with the reserved cilantro leaves and serve with hot sauce on the side.