Cook the Pasta: Bring a large pot of salted water to a boil. Cook the spaghetti according to the package instructions until al dente. Reserve 1/4 cup of the starchy pasta water, then drain the rest and set the pasta aside.
Sear the Chicken: In a large skillet over medium-high heat, melt the butter and add the minced garlic. Add the chicken pieces, seasoning them with half of the salt. Sear until the chicken is deeply golden-brown and cooked through (about 5-7 minutes). Remove the chicken from the skillet and set aside.
Build the Sauce: Reduce the skillet heat to medium. Pour in the heavy cream, chicken broth, cream cheese, and the remaining salt. Whisk continuously until the cream cheese is fully melted and the sauce begins to gently simmer.
Melt the Cheeses: Turn the heat to low and gradually stir in the shredded mozzarella and grated Parmesan cheese. Keep stirring until the sauce is completely smooth and velvety.
Combine Everything: Toss the cooked spaghetti directly into the cheese sauce until every strand is beautifully coated. If the sauce feels too thick, stir in a splash of the reserved pasta water.
Garnish and Serve: Transfer the creamy pasta to serving bowls, arrange the golden garlic chicken bites on top, and garnish generously with the fresh chopped parsley.
