Heat cast iron pan over medium-low heat. While pan is heating, slice 4 oz white button mushrooms by cutting them down the center and then slicing each half into 4-5 slices.
Once pan is hot, add 1 tablespoon butter and 1 teaspoon olive oil to pan. Add sliced mushrooms to pan. Sprinkle 1 teaspoon Herbs de Provence and ¼ teaspoon black pepper over mushrooms. Stir to cover all mushrooms with fat and spices, move to one side oft he pan to make just enough room for the chicken (if adding). Using your spatula, arrange mushrooms so they're in a single layer. Add chicken to pan. Cook for 4 minutes, or until chicken starts to look white on the bottom and mushrooms shrink. No need to stir while cooking.
Start to cook ravioli according to package directions now. Save ½-1 c of ravioli water to thicken your sauce, if needed.
After 4 minutes, add garlic and flip chicken. Stir mushrooms and arrange into a single layer. Cook for an additional 1-2 minutes.
After 1-2 minutes, add ¼ c chicken broth (or ¼ c water + ¼ teaspoon chicken bouillon paste), 2 T white wine. Stir and scrape browned bits on the bottom of the pan. Cook for about 2 minutes, to thicken slightly.
After 2 minutes, mix 1 teaspoon flour into ½ c milk and add to pan. Stir and cook until sauce thickens to heavy cream consistency. It may take 3-5 minutes. Check doneness of chicken with thermometer, it will be done once it reaches 160 degrees F.
Finally, add cooked ravioli to pan, and stir together. Add ravioli water, about 1 T at a time to thin sauce. Serve immediately and transfer any remaining dish to a storage container to refrigerate for leftovers. This ravioli dish is great as leftovers!