In a large measuring cup with a spout, combine the chicken broth, beef broth, cream, Worcestershire sauce, and seasonings and set aside. (This is the "gravy mixture")
Slice the chicken in half lengthwise to create 2-3 thinner slices. Cover with saran wrap and use the textured side of a meat mallet to pound it to ½ inch thick. Pat dry.
Season each side with salt/pepper, then sprinkle with flour and rub it over the surface of each side. (The flour gives it a little texture and prevents it from sticking to the skillet. It also thickens the gravy a little more at the end.)
Heat oil in a large skillet over medium-high heat. Sear the chicken in batches for 4-5 minutes per side, until a golden crust has developed. Set aside.
Turn the heat off. Add the wine and then set the heat to medium. Use a silicone spatula to clean the bottom and sides of the skillet, the “fond” will add more flavor to the sauce. Bring to a gentle bubble and reduce by half, about 3-4 minutes.
Melt the butter and add the flour. Stir continuously for 2 minutes, until the flour turns a light brown, and the raw flour smell is cooked off.
Add the "gravy mixture" (from step 1) in small splashes, stirring continuously. Doing this slowly is necessary to maintain the thickness of the gravy.
Bring the liquid to a gentle boil, then reduce it to a light simmer, so that it's bubbling very gently. Let it reduce and concentrate for 5-7 minutes, uncovered, stirring occasionally.
Add the chicken back to the skillet along with any juices from the plate. Spoon the sauce on top. Let it simmer and reduce for 5 more minutes, or until desired thickness is obtained. The longer it simmers, the thicker and more concentrated it will get. Maintain a very gentle simmer to ensure the chicken stays juicy. (A boil will make it tough.)