Bring a large pot of water to a boil and cook tagliatelle according to the package directions. Drain the pasta and keep it aside.
Meanwhile, melt butter in a wide skillet over medium heat until it bubbles, about one minute. Stir in the minced garlic and cook until fragrant, around one minute.
Mix in the flour promptly to create a smooth paste.
Slowly whisk in the chicken broth to avoid lumps and combine fully.
Continue by adding heavy cream gradually while whisking to keep the sauce smooth. This should take about 2 to 3 minutes.
Add the cooked pasta to the sauce along with salt, parmesan cheese, and parsley. Toss everything thoroughly until well coated.
Plate and garnish with additional parmesan and parsley if you like. Serve immediately for the best flavor.