Slice chicken in half lengthwise. Lay each slice flat on a cutting board. Cover with plastic wrap and using a meat mallet, flatten chicken breasts as flat as you can without breaking them apart.
In one shallow bowl, add eggs and season with salt and pepper. Whisk eggs until slightly frothy. In another shallow bowl, add 1 ¼ cup of Parmesan cheese and 1 tablespoon of dried oregano and mix together.
Dip each of the chicken cutlets in the egg wash first, shaking off any access egg, then into the Parmesan and organo mixture. Press each side of the chicken cutlets in the Parmesan mixture so that it is well coated on both sides.
In a large non stick frying pan, heat light olive oil and add chicken cutlets. Cook over medium heat for about 3 minutes on each side or until chicken has cooked through fully. Add more oil when needed.
Transfer chicken on a plate and set aside. In the same skillet used to cook chicken in, drizzle more oil if needed and add mushrooms. Over medium heat, cook until the mushrooms soften. Add in pepper flakes and garlic and cook for about 1 minute or until fragrant, mixing frequently.
Add butter to the mushrooms and once it melts, add 1 tablespoon of all purpose flour and whisk quickly until a smooth paste forms.
Add chicken broth, parsley flakes, Parmesan cheese, salt, and pepper. Whisk until well combined, making sure there are no lumps left from the flour.
Transfer Parmesan crusted chicken into the mushroom sauce and let it simmer on low heat for 2 minutes. The sauce will slightly thicken as it simmers.
Remove from heat and serve warm.