Flank is a delicious cut of beef when cooked medium or medium rare. The sauce here is dark, shiny, and delicious; it has a definite coffee taste that blends superbly with the wine-balsamic mixture. Depending on how salty your stock is, you can add more if desired; I have used canned stock and for me the salt level was all right. You can even prepare it with chicken or vegetable stock. It keeps refrigerated for a month! The taste of this sauce is so good you could use it as a base for other meat sauces.
Rub the flank steak with 1 teaspoon coffee, the thyme, and the pepper. Coat with the olive oil and refrigerate in a plastic zipper bag for 1 to 2 hours or overnight.
In a bowl combine the stock, wine, vinegar, brown sugar, and remaining 2 teaspoons coffee. Set aside.
When ready to cook, remove the steak from the refrigerator and allow to reach room temperature, about 10 minutes.
Heat a sauté pan over medium heat. Sprinkle the steak with salt and sear for 3 to 4 minutes on each side. Cover and cook for 5 minutes more. Remove the meat from pan and set aside covered for 10 minutes to set the juices.
Make a paste with the flour and butter.
Pour the wine mixture into the pan and bring to a boil. Add the flour-butter paste and mix well. Cook 5 to 6 minutes, until slightly thickened and no longer floury tasting.
Cut the flank steak across the grain into thin slices. Serve with the pan sauce.