Preheat your oven to 400°F. Bring a large pot of salted water to a boil and cook the elbow macaroni according to the package directions until al dente. Drain the cooked macaroni in a colander and rinse with cold water to stop the cooking process. Set aside.
In the same pot used for the macaroni, melt the salted butter over low-medium heat. Whisk in the all-purpose flour and cook for approximately 3 minutes to make a roux. Gradually whisk in the whole milk, continuing to stir over low-medium heat until the mixture thickens. Once thickened, stir in 3 cups of shredded sharp cheddar cheese and mix until fully melted and smooth. I always take my time with the sauce to keep it creamy and avoid that curdled look.
Remove the cheese sauce from the heat. Add the drained macaroni (from Step 1) to the pot with the cheese sauce and stir gently until all the noodles are evenly coated.
In a separate bowl, whisk together the eggs and salt until smooth. Pour this egg mixture into the pot with the macaroni and cheese and stir well to combine. This helps set the macaroni and cheese when baked, making it extra rich.
Pour half of the macaroni and cheese mixture into a 13" x 9" glass casserole dish. Sprinkle 1½ cups of shredded sharp cheddar cheese over the first layer. Add the remaining macaroni and cheese mixture on top, and finish with the remaining 1½ cups of shredded sharp cheddar cheese as the final layer. Sometimes I like to add a sprinkle of freshly ground black pepper between the layers for a little kick.
Cover the casserole dish with aluminum foil and bake in the preheated 400°F oven for 30 minutes. After 30 minutes, remove the foil and bake for an additional 15-20 minutes, or until the center is set and the top is lightly browned. Serve warm. Leftovers can be refrigerated.