In a small microwave-safe bowl, microwave butter for 10 seconds, or until melted.
In a medium bowl, whisk melted butter, broth, wine, and cornstarch until cornstarch has dissolved.
Bring a large skillet sprayed with nonstick spray to medium-high heat. Cook and stir mushrooms until softened, which is about 5 - 7 minutes.
Move mushrooms to the sides of the skillet. Season chicken with salt, pepper, and basil, and lay in the center of the skillet. Cook for 4 minutes, stirring mushrooms occasionally. (You can also move mushrooms to another dish and add them again with the broth mixture.).
Flip chicken. Give broth mixture a stir and add to the skillet. Stirring mushrooms occasionally, cook until sauce has thickened and chicken is cooked through, about 5 minutes.