In a large pot of boiling salted water, cook pasta according to package instructions; drain well and set aside.
Lay the breasts down on a cutting board and use a sharp knife parallel to the cutting board to cut them (carefully) in half. Season both sides with salt and pepper.
Heat a small amount of oil - just enough to coat the bottom of a skillet or non-stick pan over medium heat. Brown the chicken on both sides until golden brown then remove and set aside.
Add the remaining oil to the pan along with the mushrooms, shallots, and garlic. Sauté until the mushrooms start to soften (about 3-4 minutes).
Stir in the broth and thyme. Bring to a simmer; stirring occasionally for about 6-8 minutes. Return the chicken to the pan and add in the heavy cream and butter, simmer until the sauce reduces and starts to become thick and creamy.
Toss in the pasta; adjust the seasoning with salt and pepper to taste. Serve with bread. Garnish with parmesan and thyme.