In a bowl, combine the balsamic vinegar, olive oil, minced garlic, and fresh basil. Add a pinch of salt and pepper. Place the chicken breasts in the marinade and let them soak for at least 15 minutes (or up to 2 hours in the fridge).
Heat a skillet over medium heat. Remove the chicken from the marinade, reserving the marinade for later. Cook the chicken breasts for about 6-7 minutes on each side or until they are fully cooked and have a nice golden color. Once cooked, remove from the skillet and set aside to rest.
In the same skillet, melt the butter over medium heat. Add the diced shallots and sliced mushrooms. Sauté for about 5-6 minutes until the shallots are translucent and the mushrooms are tender. Stir in the minced garlic and cook for an additional minute.
Pour in the reserved marinade and bring it to a simmer. Add the heavy whipping cream and let it cook for about 3-4 minutes, stirring occasionally. Add the grated parmesan cheese and frozen peas, and continue to stir until the cheese is melted and the sauce is creamy. Season with salt and pepper to taste.
While the sauce is simmering, cook the fettuccine according to package instructions in a large pot of salted boiling water. Drain and set aside.
Slice the cooked chicken and add it to the sauce along with the cooked fettuccine. Toss everything together to coat the pasta well in the creamy sauce.
Plate the Pasta Carrabba and sprinkle with fresh grated parmesan cheese. Garnish with additional fresh basil if desired. Enjoy your delicious meal!