Season the tenderloins with salt, pepper, paprika, and garlic powder.
Dredge the seasoned chicken in flour and shake off any excess.
Heat three tbsps of olive oil in a large skillet and brown the tenderloins on both sides, about 3 minutes on each side. Transfer to a 9x13-inch baking dish.
In the same skillet, heat the remaining tbsp of oil, and saute the mushrooms, onions, and garlic with the oregano, and thyme until the mushrooms are brown and the onions translucent.
Spread this mixture over the chicken tenderloins.
Preheat the oven to 350 F and make the sauce:
In a large skillet, melt 3 tbsp of butter and add 3 tbsp of flour. Cook the flour until slightly golden, about 2 minutes.
Carefully and slowly, whisk in the chicken broth, white wine, lemon juice, salt, and pepper. Make sure there are no lumps left in the sauce.
Bring to a boil, reduce to a simmer and pour in the half and half. Cook until slightly thick.
Pour the sauce over the chicken and mushrooms. Cover with foil, and bake for 45 mins.