1Boil wine, chicken broth and beef broth in heavy large saucepan over high heat until mixture is reduced to 2 cups, about 1 hour. (Can be prepared 1 day ahead. Cover and refrigerate.)
2Mix butter and flour in small bowl. Heat 1 tablespoon olive oil in heavy large skillet over medium-high heat. Sprinkle steaks with salt and cracked pepper.
3Saute steaks until medium-rare, about 4 minutes per side. Transfer to plate.
4Add shallots, garlic and thyme to skillet; stir 30 seconds. Add 1 1/2 cups reduced wine mixture to skillet (reserve remainder for another use). Bring mixture to boil, scraping up any browned bits. Add butter mixture and whisk until smooth. Boil sauce until thick enough to coat spoon, about 2 minutes.