Preheat oven to 375°F. Spray a 9x13-inch baking dish with cooking spray and set aside.

Cook the elbow macaroni according to package directions and drain. Rinse the noodles with cold water to cool and stop the cooking process and allow them to drain.

Place the Velveeta and the milk into a medium saucepan and heat over medium-low heat until the cheese is melted, stirring often. Remove from the heat and set aside.

Crack the eggs into a small bowl and whisk until combined. Add a scoop (about ⅓ to ½ cup) of the cheese sauce to the eggs to temper them, whisking well as you add the cheese sauce. Quickly add the egg mixture to the remainder of the cheese sauce in the pan, whisking until well combined. 

Place half of the macaroni into the prepared pan. Season with salt and pepper. Slice half of the stick of butter into thin pieces and place the butter pats evenly on top of the macaroni. Sprinkle half of the Cheddar and half of the Monterey Jack cheese evenly over the top. Ladle or pour half of the cheese sauce evenly over the top. Repeat the layers - macaroni, salt and pepper, butter, Cheddar, and Monterey Jack, cheese sauce. 

Bake uncovered for 30-35 minutes or until bubbly and the top is lightly browned.