Bring a large pot of water to a boil and add 1 tablespoon of salt. Cook the pasta according to package instructions. Before draining, reserve 1 cup of pasta water for the sauce.
In a large saucepan, heat the olive oil over medium heat. Add the garlic and cook for 30 seconds to 1 minute until fragrant. Stir in the tomato paste, mixing it with the oil and garlic.
Slowly whisk in the heavy cream until fully incorporated, then pour in the chicken broth. Stir in the Parmesan cheese and seasonings.
Gradually add 1/4 to 1/2 cup of the reserved pasta water, stirring to combine.
Add the cooked pasta to the sauce, stirring until well coated. If needed, add more pasta water to reach your desired consistency.
Taste and adjust seasonings as needed. Garnish with additional Parmesan cheese before serving.