Grate the Parmesan cheese and set it aside to bring to room temperature.
In a large skillet, melt 2 tablespoons of butter over medium heat.
Add the minced garlic and cook for 1-2 minutes, stirring occasionally until fragrant.
Pour in the chicken broth, along with any optional seasonings. Gradually stir in the milk and bring the mixture to a gentle boil.
Add the angel hair pasta. You can break the noodles in half to fit the skillet, or use tongs to guide the noodles into the pan as they soften.
Let the pasta simmer for 4-5 minutes, stirring occasionally to prevent the noodles from sticking together. Reduce the heat to low once the pasta is al dente.
Stir in the remaining 1 tablespoon of butter, ensuring the pasta is fully coated.
Gradually incorporate the Parmesan cheese, stirring until the sauce becomes smooth. The sauce will thicken as it stands and the pasta absorbs more of the liquid.
Garnish with fresh parsley and serve immediately, perhaps accompanied by Garlic Bread with Cheese for an extra indulgence.