Combine the flour, salt, and pepper in a large plate or wide-bottom bowl. Dredge the chicken in the flour on both sides. Add 4 tablespoons of olive oil to a large skillet and cook the chicken on medium heat about 5-7 minutes per side, or until nicely browned. Set the chicken aside on a plate (it's OK if the chicken is not fully cooked yet).
Add 1 tablespoon of oil to the same skillet and saute the mushrooms over high heat for about 5 minutes, or until they start to sweat. Add the sliced onions, turn the heat to medium-low, and allow to cook for about 5 minutes, stirring occasionally.
Add the remaining 1 tablespoon of olive oil to the skillet. Add the minced garlic, thyme, and oregano. Saute over medium heat for 2-3 minutes, but don't let the garlic brown. Add the chicken broth and white wine and bring to a simmer.
Add the chicken back to the skillet. Cover and cook over medium heat for 10-15 minutes, or until the chicken is fully cooked. Sprinkle with freshly grated Parmesan cheese and cover with a lid for 2 minutes, or until the cheese is fully melted. Remove from heat and serve with your favorite side dishes.