Melt 1 tablespoon of the butter in the Dutch oven over medium-high heat.
Add the cubed chicken and sliced mushrooms and cook, stirring occasionally, until the chicken is no longer pink and mushrooms are softened, about 5–7 minutes.
Season the chicken and mushrooms with 1/2 teaspoon salt, 1 teaspoon pepper, and 1 teaspoon garlic powder (if using). Remove the mixture from the pot and set aside.
Add the remaining 3 tablespoons of butter to the pot and melt over medium heat, then whisk in 1/4 cup all-purpose flour to make a roux and cook for 1–2 minutes.
Gradually whisk in 3 cups chicken broth and 1 cup milk until smooth, bring the sauce to a gentle boil, and allow it to thicken slightly while stirring.
Reduce heat to low, return the chicken and mushrooms to the pot, add the uncooked 8 ounces spaghetti (break in half if needed to fit), and stir to combine, ensuring pasta is submerged.
Cover and cook over low heat for 20–25 minutes, stirring often to prevent sticking, until the pasta is al dente and the sauce has thickened.
Remove from heat, stir in or sprinkle 1/4 cup Parmesan cheese and 2 tablespoons chopped parsley, taste, and adjust seasoning if needed, then serve.
