Mix Tuna Filling: In a bowl, combine tuna, mayonnaise, Dijon mustard, cilantro, green onions, lime zest, chili powder, salt, and pepper.
Prepare Tortillas: Lay out tortillas on a flat surface. Spread tuna mixture evenly over four tortillas, leaving a small border around the edges.
Add Cheese: Sprinkle shredded cheddar cheese evenly over tuna mixture.
Top and Press: Place remaining tortillas on top of cheese-covered tortillas. Press down gently to help filling adhere.
Heat Pan: Heat a non-stick skillet over medium heat. Add 1 Tablespoon butter and let it melt, coating bottom of the pan.
Cook Quesadillas: Place one quesadilla in skillet. Cook for about 2-4 minutes on each side, or until tortillas are golden brown and cheese is melted. Add remaining 1 Tablespoon butter and repeat with remaining quesadillas, adding more butter as needed.
Cut and Serve: Remove quesadillas from skillet and let cool slightly. Cut each quesadilla into triangles and serve warm.