Place the drained chickpeas in a medium mixing bowl and use a fork or potato masher to mash them. You want about half the chickpeas broken down into a spreadable consistency while the other half remains chunky. This typically takes 30 to 45 seconds of mashing. The texture should resemble tuna salad with visible chickpea pieces throughout.

Add the vegan mayonnaise or Greek yogurt, Buffalo hot sauce, fresh lemon juice, diced celery, grated carrot, red onion, parsley, garlic powder, and smoked paprika to the bowl. Stir everything together until thoroughly combined and the chickpeas are evenly coated. The mixture should look vibrant orange with flecks of green and red throughout. Season with salt and black pepper to taste.

Lay the tortillas flat on a clean work surface. Distribute the shredded lettuce, diced tomatoes, and cheese evenly across the center of each tortilla, leaving about 2 inches of space on each side for folding.

Spoon about 1/2 to 3/4 cup of the Buffalo chickpea mixture over the vegetable layer on each wrap, depending on tortilla size. Spread it gently to within 1 inch of the filling edge using the back of your spoon. Drizzle with ranch or blue cheese dressing if using, but avoid overdoing it or the wraps may get soggy.

Fold the sides of each tortilla inward, then roll tightly from the bottom up, keeping the filling secure inside. The tortilla should wrap completely around the filling without any gaps. If your tortilla cracks, warm it for 10 seconds in the microwave to make it more pliable.

Slice each wrap in half diagonally for easier eating, or wrap tightly in foil for portable lunches. Serve immediately for the best texture, or refrigerate for up to 24 hours.