Add olive oil and 2 tbs of butter to a large frying pan and heat over medium-high heat until butter is melted.
Meanwhile, place chicken tenders in sealed plastic storage bag or wrap with plastic wrap and flatten to ¼” thickness with a meal mallet or rolling pin. Season with salt and pepper and coat lightly in flour.
Working in batches (do not overcrowd pan), brown chicken in pan for about 2-3 minutes a side. Do not worry about cooking the chicken through- it will finish in the sauce later, Once chicken is browned lightly on both sides, remove to a plate and continue until all chicken is browned.
Reduce heat to medium low and add remaining 2 tbs butter, sliced mushrooms, thyme, salt and pepper. Cook, stirring occasionally until mushrooms are softened and have released most of their liquid, about 8-10 minutes. Add garlic and cook until fragrant, about 1 minute. Add the wine and bone broth, and season once more with salt and pepper, if needed (taste as you go!).
In a bowl or liquid measuring cup, whisk together ¼ cup of milk and 4 teaspoon flour. Stir into sauce.
Place chicken back into pan and cook 5 minutes, stirring occasionally until sauce is thickened.
Let rest 5 minutes and serve with crusty bread, pasta, roasted potatoes or mashed potatoes and veggies. Enjoy!