Cook and drain pasta according to package directions for al dente. Set aside.
Combine 1/2 cup of flour, 1 tsp. of salt and 1/4 tsp. pepper in a shallow bowl.
Heat olive oil with 2Tbsp. of butter in a large skillet over medium heat.
Dredge the chicken in the flour mixture and place it into the pan. Cook chicken until it's browned on both sides and cooked through the center, about 7-8 minutes per side. Remove from pan.
Add the remaining butter. Stir in 1 Tbsp. of flour, 1 tsp. of salt, 1/2 tsp. of pepper and the sliced mushrooms. Cook until the mushrooms have softened and released liquid.
Stir in the garlic and cook until sizzling.
Pour in the wine. Bring to a boil over medium-high heat, scraping any browned bits off the bottom of the pan. Reduce heat and simmer until the liquid is reduced by half.
Stir in the cream and chicken broth. Bring to a boil, then reduce heat to low. Put the chicken back into the pan and simmer 15 minutes.
Serve the chicken and sauce over pasta.