Start by finely dicing the yellow onion, carrots, and celery, and mincing the garlic. Grate the sharp cheddar and Monterey Jack cheese using a box grater until finely shredded. Set everything aside.

In a large pot, melt 2 tablespoons of unsalted butter over medium heat. Add the diced onion, carrots, and celery, sautéing them for 8-10 minutes until softened and fragrant. Stir in the minced garlic, dried thyme, smoked paprika, and dry mustard powder; cook for an additional minute until the spices become aromatic.

Sprinkle in 1/4 cup of all-purpose flour, stirring well to combine and create a roux. Gradually whisk in 4 cups of low-sodium chicken broth, then pour in 1 cup of whole milk and 1 cup of heavy cream. Season with salt and pepper, then bring the mixture to a gentle simmer, allowing it to thicken and become creamy, about 5-7 minutes.

Once your soup base is bubbling gently, reduce the heat to low and gradually add the grated cheeses. Stir continuously until the cheese melts completely and creates a smooth, creamy texture.

In a separate pot, bring salted water to a boil and add 1 cup of elbow macaroni. Cook the pasta until al dente, usually around 6-8 minutes. Drain the macaroni and set it aside.

Stir the cooked chicken into the creamy soup base, followed by the drained macaroni. Allow everything to simmer together for a couple of minutes, ensuring the dish is heated through and flavors are well combined. Serve hot, garnished with fresh parsley, chives, or extra cheese for an inviting presentation.