Heat a large nonstick or cast-iron skillet over medium-high heat and lightly spray with oil.
Lay tortillas flat in the pan. Spread a thin, even layer of chicken mixture directly onto one side of each tortilla, pressing firmly.
Cook chicken-side down for 4–5 minutes until deeply golden and crisp.
Flip, place one slice of sharp cheddar directly on the hot chicken, and cook 1–2 minutes more until melted and the tortilla is lightly crisp.