1Melt 1 tablespoon butter in heavy medium saucepan over medium heat. Add shallots and saute until tender, about 4 minutes. Add brown sugar; stir 1 minute. Add chicken broth, beef broth and Cognac. Simmer until sauce is reduced to 1/2 cup, about 20 minutes. Add cream. (Can be made 1 day ahead. Cover; chill.)
2Sprinkle steaks with salt and pepper. Melt 1 tablespoon butter in heavy medium skillet over medium-high heat. Add steaks; cook to desired doneness, about 4 minutes per side for rare. Transfer steaks to plates. Add sauce to skillet; bring to boil, scraping up any browned bits. Season to taste with salt and pepper.
3Slice steaks; fan slices on plates. Top with sauce and garnish with chives.