Start by bringing a large pot of salted water to a rolling boil. Add the 8 ounces of linguine and cook according to package instructions until al dente, usually about 8-10 minutes. Once cooked, reserve a cup of pasta water, then drain the rest and set the pasta aside.
In a large skillet, melt 1 tablespoon of butter over medium heat. Add in 1 teaspoon of flour, stirring continuously for about 1 minute until it forms a roux.
Add the minced garlic (2-3 cloves) to the skillet and sauté for about 30 seconds, until fragrant. Be careful not to burn the garlic.
Pour in 1/4 cup of chicken broth followed by 1 cup of heavy cream. Stir well and let it simmer for 2-3 minutes.
Stir in 1/3 cup of freshly grated parmesan cheese, allowing it to melt into the sauce. Season with salt and pepper to taste.
Add the cooked linguine to the skillet, tossing to coat it in the creamy sauce. If desired, sprinkle with chopped fresh parsley and serve immediately.