In a large deep skillet or wide pan, pour 2½ cups chicken broth, then add ½ cup heavy cream, ⅔ cup whole milk, 1 tablespoon butter, and 3–4 cloves garlic (minced). Season with ½ teaspoon sea salt and ½ teaspoon cracked pepper. Heat over medium until the liquid comes to a light boil.

Add 8 oz thin spaghetti to the pan, pushing the strands down so they are mostly submerged (break the strands if necessary to fit). Increase heat briefly as needed to bring the liquid back to a gentle boil.

As soon as the liquid begins to boil, reduce heat to medium-low (a gentle simmer). Cook the pasta, stirring frequently and turning the strands so they cook evenly, until the spaghetti is al dente, about 8–10 minutes.

If the liquid is absorbing too quickly and the pasta is not yet al dente, add up to an additional ½ cup chicken broth (for a total of up to 3 cups), a splash at a time, to keep the pasta moist.

When the pasta has about 2–3 minutes left, stir in 1½–2 cups cubed cooked chicken so it can heat through with the pasta.

Once the pasta is al dente and the chicken is heated, remove the pan from the heat. Stir in ⅓ cup grated Parmesan until the sauce becomes creamy. If the sauce is too thick, add small tablespoons of the ⅔ cup whole milk until you reach the desired consistency.

Taste and adjust seasoning if needed. Serve immediately, sprinkled with the 3 tablespoons chopped fresh parsley.