Sift together the flour, chicken seasoning, tarragon, seasoned salt, garlic powder, onion powder, dried Italian seasoning and black pepper. Reserve ¼ cup and set aside.
Pat dry chicken tenders with paper towel. Dredge chicken on all sides in the seasoned flour.
Heat a few drizzles of olive oil in a large 12-inch skillet over medium-high heat. Cook the tenders for 2 minutes per side or until the juices run clear. Remove to a platter and keep warm.
Add a few drizzles of olive oil and tablespoon of butter to the pan. Cook sliced mushrooms and onions. for 5-7 minutes until softened and browned. Scrape any brown bits from the bottom of the pan. Season with salt and black pepper to your taste.
Sprinkle the reserved ¼ seasoned flour over the cooked mushrooms and onions, Stir until all liquid is absorbed.
Whisk in the the milk. Bring to a simmer stirring constantly and cook until thickened. Lower the heat and allow to bubble gently for 5 minutes.
Pour over the chicken pieces and serve.