Preheat oven to 475 degrees Fahrenheit. Place a wire rack on a large baking sheet and brush the rack with oil.
Cut the chicken into small strips, about 2 inches long.
On a rimmed plate, spread out the flour.
In a wide bowl, beat the eggs together.
On another rimmed plate, combine the Panko and Parmesan. Coat each chicken piece with flour, then egg, and Panko Parmesan. Arrange in a single layer on the greased wire rack.
Bake in preheated oven until the chicken is crispy, golden brown, and cooked through, 10-15 minutes.
While the chicken is baking, melt the cream cheese in a small saucepan over medium-low heat. Whisk in the milk, garlic, and olive oil. Once smooth, add the shredded cheddar. Add more milk, as needed, if the sauce is too thick.
Drizzle the cheese sauce over the chicken or serve on the side. Top with parsley.