Preheat the Oven:Preheat your oven to 400°F (200°C). Prepare a baking sheet by either lining it with parchment paper or applying a light coat of oil to prevent sticking.
Prepare the Chicken: Trim and butterfly the chicken breasts or thighs to create evenly sized portions. Season both sides of the chicken with salt, pepper, onion powder, garlic powder, and oregano if desired.
Set Up the Breading Station: In three separate shallow dishes, place the flour in one, beaten eggs in the second, and the mixture of shredded cheddar cheese and cheese cracker crumbs (or panko breadcrumbs) in the third.
Bread the Chicken: Coat each piece of chicken in flour, making sure to shake off any extra. Dip it into the beaten eggs, allowing the excess to drip off, and then coat it generously in the cheddar and cracker crumb mixture. Press the coating onto the chicken to ensure it sticks well.
Bake the Chicken: Place the breaded chicken pieces onto the prepared baking sheet in a single layer. Bake in the preheated oven for 20-25 minutes, or until the chicken is golden brown and cooked through (internal temperature of 165°F/75°C). To achieve an added crunch, consider broiling the chicken for the final 2-3 minutes, watching it carefully to prevent any burning.
Serve: After the chicken is finished cooking, take it out of the oven and allow it to rest for several minutes. Serve it warm with your favorite sides, such as mashed potatoes, a fresh salad, or roasted vegetables.