Preheat the oven to 400°F.
Cut each boneless skinless chicken breast into 3 equal pieces.
Place the crushed Ritz crackers or Cheese-Its crackers in a shallow dish.
Add the shredded cheddar cheese and garlic powder to the crushed crackers.
Toss the cracker mixture until the cheese and garlic powder are evenly distributed.
In a separate shallow bowl, combine the beaten eggs and milk.
Dip each chicken piece into the egg and milk mixture, allowing any excess liquid to drip off.
Transfer the chicken to the cracker and cheese mixture.
Press the crumb mixture gently onto the chicken to coat it evenly.
Repeat the coating process by dipping each coated chicken piece back into the egg mixture, then into the cracker mixture a second time.
Gently press the crumbs onto the chicken to help the coating adhere.
Arrange the coated chicken pieces on a baking sheet in a single layer, leaving space between each piece.
Sprinkle the coated chicken evenly with dried parsley.
Bake for 20 to 25 minutes, or until the coating is golden and the chicken reaches an internal temperature of 165°F.
While the chicken bakes, prepare the cheese sauce.
Place the shredded cheddar cheese and cornstarch in a small microwave-safe bowl.
Toss until the cheese is evenly coated with cornstarch.
Add the evaporated milk to the cheese mixture.
Microwave for 45 seconds.
Stir the sauce thoroughly.
Continue microwaving in 30-second increments, stirring after each interval, until the sauce is thick, smooth, and creamy. The total heating time should be approximately 90 seconds, depending on the microwave.
Remove the chicken from the oven once fully cooked.
Serve the chicken warm with the cheese sauce on the side or drizzled over the top.