Place the chicken breasts between wax paper and pound with a mallet to flatten. Cut each piece in half lengthwise. Cover with plastic wrap and refrigerate until firm.
In a small frying pan, heat 1 tablespoon of the olive oil over medium heat. Add the shallots and saute for about 3 minutes. Add the mushrooms and cook for 2 minutes more, stirring occasionally.
In a small bowl, whisk together the flour and wine until all the lumps are gone. Add the flour mixture to the shallots and mushrooms. Stir in the chicken stock and cook over medium-high heat. Stir until the sauce thickens, about 5 minutes. Remove from heat and add the rosemary.
In a large, nonstick skillet, heat the remaining 1 tablespoon of olive oil over medium heat. Add the chicken and saute until no longer pink or until a thermometer inserted into the chicken reads 170 F, about 5 minutes.
To serve, transfer 2 chicken breast halves onto each plate. Spoon mushroom sauce over the chicken and garnish with parsley. Serve immediately.