Combine the chili powder, cumin, smoked paprika, garlic powder, onion powder, dried oregano, salt, and black pepper in a small bowl and stir to create a taco seasoning blend.
Heat the olive oil in a large skillet over medium heat until shimmering, then add the ground beef and cook, breaking it up with a spatula, until browned and cooked through.
Drain off any excess grease if needed, sprinkle the taco seasoning evenly over the meat, pour in the water or beef broth, and simmer while stirring until the liquid is mostly absorbed and the meat is well coated and fragrant.
Taste the seasoned beef and adjust the salt or spices to your preference, then turn off the heat and set the skillet aside to slightly cool while you prepare the toppings.
Prepare the lettuce by shredding it finely and patting it dry with paper towels, slice or mash the avocado, and set out the shredded cheese, sour cream, and salsa for easy assembly.
If you want an extra crunchy cheese layer, heat a small nonstick skillet over medium heat and sprinkle about 1/4 cup of shredded cheese into an even circle slightly smaller than your tortilla.
Cook the cheese round until the edges are deeply golden and the center has set, then carefully slide it onto a plate to crisp as it cools and repeat to make as many cheese rounds as you need.
Warm the low-carb tortillas briefly in a dry skillet or microwave until pliable so they fold easily without cracking.
Place a warm tortilla on a work surface and sprinkle about 1/2 cup of shredded cheese in the center, leaving a wide border around the edges to allow for folding.
Spoon about 1/4 of the seasoned beef on top of the cheese, then add a crunchy cheese round if using, followed by a small handful of shredded lettuce, a few slices or spoonfuls of avocado, and a dollop of sour cream and salsa.
Fold the tortilla edges up and over the filling, working around in a circle to create overlapping pleats until the filling is completely enclosed in a compact wrap.
Repeat the layering and folding process with the remaining tortillas and filling ingredients to form four crunch wraps in total, taking care not to overfill so they stay sealed.
Heat a large skillet or griddle over medium heat and add a small amount of butter or ghee, swirling to coat the surface evenly.
Place one or two crunch wraps seam side down in the hot skillet and press gently with a spatula to help the folds seal and the cheese near the tortilla start to melt.
Cook the wraps until the bottoms are deeply golden and crisp, then carefully flip and cook the second side until equally browned and the cheese is fully melted through the center.
Transfer the toasted wraps to a cutting board and let them rest for a minute to set, then slice in half if desired and serve hot with extra sour cream, avocado, or salsa on the side.