Heat the olive oil in a large skillet.
Mix the 1/4 cup of flour with the salt and pepper. After halving the breast half into thinner slices, and pounding them thin dredge the chicken in the flour mixture. Cook the chicken through and set aside on a platter.
Toss the mushrooms and onions into the skillet and cook until tender. Melt in the 2 tbsps of butter (more or less depending on the remaining olive oil), add the 3 tbsps of flour and cook everything together, stirring constantly and picking up the bits on the bottom of the skillet. Stir in the wine and cook for a minute then add the chicken broth and thyme. Cook until thickened, add in the parsley, and then put the chicken back in to heat through for a few minutes. Serve.