In a bowl, combine the drained tuna, mayonnaise, lemon juice, finely diced celery, and grated red onion. Add a good pinch of salt and several cracks of black pepper. Give it a taste and adjust – the filling should be creamy and bright, with a distinct crunch from the celery.
Place a large non-stick skillet over medium heat. Give it a full minute to warm up before adding anything. A drop of water should sizzle gently on the surface – not aggressively, just a steady dance.
Lay a tortilla flat on the cutting board. Sprinkle a generous layer of shredded cheese (about 1/4 cup) all over the surface – edge to edge, but leave a 1-inch border around the rim. This is your moisture barrier.
Spoon half the tuna salad (about 1/2 cup) down the center of the tortilla in a straight line. Top with another 1/4 cup of cheese on top of the tuna. Don't overstuff – a tightly wrapped tortilla cooks more evenly and stays sealed.
Fold the sides of the tortilla inward over the filling, then roll it away from you into a tight cylinder, tucking the seam underneath. The cheese barrier will feel slightly tacky, which helps seal the edge.
Place it seam-side down in the hot pan. Press gently with the spatula for 10 seconds to encourage even browning. You should hear a steady, low sizzle. If it's loud and popping, turn the heat down.
Cook for 2-3 minutes per side, until the tortilla is deeply golden and crisp in patches, and the cheese is visibly oozing from the edges. The wrap should feel firm when you press on it.
Transfer the wrap to the cutting board and let it rest for exactly 60 seconds. This lets the cheese set slightly so the filling stays put when you cut into it.
Slice diagonally with a serrated knife – it cuts cleanly without squishing the filling. Serve immediately.
Notes
Prep the tuna salad up to 3 days in advance. Reheat leftovers in a dry skillet over medium heat for 2 minutes per side – not the microwave. For gluten-free, use large GF tortillas. For dairy-free, use a good melting dairy-free cheese.