Heat a non-sticking pan sprinkled with 1 tablespoon of salt. When it is hot lower the flame, add the chicken breast and cover. After 8 minutes flip chicken over, cover and cook for another 8 minutes. Wrap the chicken breasts in aluminium foil and let it rest for 5-6 minutes.
In the meantime heat 7 quarts of water to boiling and add 2 tablespoons of salt. Cook the Tagliatelle according to package instructions and drain, reserving 1 cup of the cooking water.
Shred the chicken breasts. Melt the butter in the pan and toss the shredded chicken for 3-4 minutes until golden brown and crispy. Set aside.
Heat the Alfredo sauce in a separate large skillet, then add the pasta and toss gently to incorporate, adding cooking water to the pan a little at a time as needed to achieve a cream-like consistency. Plate the Tagliatelle and top with crispy chicken, chopped parsley, freshly ground black pepper and grated Parmigiano Reggiano cheese.