Pat 4 skinless, boneless chicken breasts dry with paper towels. Working with 1 breast at a time, place chicken between 2 sheets of plastic wrap or wax paper. Using a meat mallet, rolling pin, or heavy skillet, pound to 1/2" thick. Season all over with kosher salt and freshly ground black pepper.
Pulse 3 cups cheese crackers in a food processor or blender until the consistency of sand. Transfer to a shallow bowl; stir in a pinch of salt.
Place ½ cup all-purpose flour in another shallow bowl.
Beat 2 large eggs and 1 Tbsp. Dijon mustard in a third shallow bowl to blend.
Working one at a time, dredge chicken in flour, shaking off excess, then dip in egg mixture, letting excess drip back into bowl. Dredge in cracker mixture, pressing to adhere. Transfer to a baking sheet.
Preheat air fryer to 400F. Spray the basket and top of the chicken with oil. Place chicken breasts 1 or 2 at a time (whatever fits comfortably) and cook for 5 minutes. Flip the breasts, spray with oil and cook for an additional 4 minutes. Remove breasts from air fryer basket, set aside and repeat with remaining chicken.
Serve chicken with lemon wedges for squeezing over.
Notes
These chicken breasts can also be pan-fried in vegetable oil.