Warm the skillet over medium heat until hot, and briefly toast each tortilla for about 10 seconds per side until they are pliable and slightly toasted, releasing a toasty aroma.
Spread a thin layer of spicy mustard or mayonnaise over the center of each tortilla, covering about two-thirds of the surface to add flavor and moisture.
Layer the leftover turkey slices evenly over the sauce, placing about 1-2 slices per wrap, making sure to distribute the meat for balanced bites.
Sprinkle shredded cheddar or mozzarella cheese over the turkey, allowing it to melt slightly when cooked, adding creaminess and savory flavor.
Add a handful of shredded lettuce and a few thin cucumber slices on top, providing a crisp, fresh contrast to the tender turkey and melty cheese.
Sprinkle a pinch of smoked paprika or cumin over the fillings for a warm, smoky note, enhancing the overall flavor.
Fold the sides of the tortilla inward and tightly roll from one edge to the other, creating a compact wrap that holds all the fillings securely.
Place the assembled wrap seam-side down in the hot skillet and cook for 2-3 minutes until the bottom is golden brown and crispy, pressing gently with a spatula.
Flip the wrap carefully and cook the other side for another 2-3 minutes until equally golden and crispy, ensuring the cheese is melted and the filling is heated through.
Remove the wrap from the skillet and let it rest for a minute, allowing the filling to settle and making it easier to slice without spilling.
Slice the wrap in half diagonally, revealing the crispy exterior and colorful, steaming interior, then serve immediately with extra sauce or sides of your choice.
