Heat an oven proof pan over medium high heat. Add the vegetable oil. Once it is nice and hot, sear the chicken breasts on both sides and then place in the oven to cook for 20-25 minutes. You want the chicken to reach an internal temperature of 165 degrees but cooking time might vary slightly depending on the thickness of the breast.
Turn the heat down to medium low and add the skim milk and evaporated milk. Cook for about 7 minutes until it begin to thicken. Turn off the heat and stir in the cheese. Taste and season with salt and pepper.