Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish and set aside.
Bring a large pot of water to boil. Mix in chicken bouillon base. Add the elbow macaroni and cook until al dente, about 7-8 minutes. Drain the macaroni and set it aside.
In a large saucepan, melt the butter over medium heat. Stir in the milk and half-and-half, and heat until warm, but not boiling.
In a separate bowl, whisk the beaten eggs. Gradually add a small amount of the warm milk mixture to the eggs, whisking constantly to temper them (this prevents the eggs from scrambling). Once tempered, slowly pour the egg mixture back into the saucepan with the milk mixture, whisking constantly.
Add the salt, black pepper, garlic powder, onion powder, paprika, mustard powder, and cayenne pepper to the milk mixture. Stir until the seasonings are well combined, then taste the sauce and adjust the seasoning to your preference. Add more salt, pepper, garlic powder, onion powder, paprika, or cayenne as desired for a more robust flavor.
Gradually add the Velveeta cubes to the saucepan, stirring until melted and smooth.
Stir in 1 ½ cups of the shredded cheddar cheese, ½ cup of the Monterey Jack cheese, and ½ cup of the mozzarella cheese. Continue stirring until all the cheese is melted and the sauce is smooth and creamy.
Remove the saucepan from the heat and stir in the sour cream until fully incorporated.
Pour the cooked macaroni into the prepared baking dish. Pour the cheese sauce over the macaroni and stir to ensure all the pasta is evenly coated with the sauce. Top with the remaining cheese.