Season the chicken fillets with salt and pepper, and sprinkle with flour.
Add 2 Tbsps of the olive oil and 1 Tbsp of the butter to a pan on medium-high heat until the butter is melted.
Place the chicken breasts in the pan and cook until golden brown and turn. Add another 1 Tbsp of butter to the pan and cook the medallions until the inside temperature reaches 75ºC (165ºF).
Remove chicken from the pan, and set aside. Add the remaining 1 Tbsp olive oil to the pan, add the shallots and sauté, add the mushrooms and sauté until soft. Add the tomatoes, then add the chicken broth and white wine. Cook down until the liquid is reduced significantly. Add 1/4 cup of butter and melt, stirring into the sauce.
Add the chicken back into the pan, turning to coat. Place the pasta in a large shallow dish, then top with sauce and chicken. Serve.