The history of cooking and serving meat with spiced sauces dates back to ancient times. Sauces were employed to tenderize cuts and add flavour. Pepper was highly favored by Ancient Roman and Medieval cooks and figured prominently in many recipes. According to the Larousse Gastonomique, Sauce Diane (Diana...aka Artemis...a powerful mythological huntress) is traditionally associated with venison.
"Steak Diane was originally a way of serving venison, and its sharp sauce was intended to complement the sweet flavor of deer meat. It was named for Diana, Roman goddess of the hunt, and since Diana was also the moon goddess, the small pieces of toast used to sop up the delicious juices are traditionally cut in crescent shapes." Rare Bits: Unusual Origins of Popular Recipes, Patricia Bunning Stevens [Ohio University Press:Athens OH] 1998 (p. 100)
Evidence suggests Steak Diane is an American invention of the late 1950s/early1960s, when French cooking (think Julia Child & the Kennedy White House menus) was all the rage. Rich wine sauces and flamboyant presentation were the norm for many top restaurants. If Steak Diane is an American recipe, then New York City is the most likely place or origin. Jane Nickerson's article "Steak Worthy of the Name," (New York Times, January 25, 1953 p. SM 32) offers three likely candidates: "The Drake Hotel, the Sherry-Netherland Hotel and the Colony Restaurant each said, not knowing that any other dining place had done so, that their patrons praised their steak Diane. Nino of the Drake claimed he was the first to introduce this dish to New York and, in fact, to the entire United States. Essentially it consists of steak cooked in butter and further seasoned with butter mixed with fresh chives; usually the beef is pounded thin. The chef of each establishment has his own version."
For the Sauce Base: Heat oil and tomato paste in Dutch oven over medium-high heat; cook, stirring constantly, until paste begins to brown, about 3 minutes. Add onions, carrot, and garlic; cook, stirring frequently, until mixture is reddish brown, about 2 minutes. Add 2 tablespoons water and continue to cook, stirring constantly, until mixture is well browned, about 3 minutes, adding remaining water when needed to prevent scorching. Add flour and cook, stirring constantly, 1 minute. Add wine and, using a heatproof rubber spatula, scrape up browned bits on bottom and sides of pot; bring to boil, stirring occasionally (mixture will thicken slightly). Add beef and chicken broths, peppercorns, thyme, and bay; bring to boil and cook, uncovered, occasionally scraping bottom and sides of pot with spatula, until reduced to 2 1/2 cups, 35 to 40 minutes.
Strain mixture through fine-mesh strainer, pressing on solids to extract as much liquid as possible; you should have about 1 1/4 cups.
For the steaks: Heat 1 tablespoon oil in 12-inch heavy-bottomed skillet over medium-high heat until smoking. Meanwhile, season steaks with salt and pepper. Place 2 steaks in skillet and cook until well browned, about 1 1/2 minutes. Following illustrations below, flip steaks and weight with heavy-bottomed pan; continue to cook until well browned on second side, about 1 1/2 minutes longer. Transfer steaks to large platter and tent with foil. Add 1 tablespoon oil to now-empty skillet and repeat with remaining steaks; transfer second batch of steaks to platter.
For the sauce: Off heat, add 1 tablespoon oil and shallots to now-empty skillet; using skillet's residual heat, cook, stirring frequently, until shallots are slightly softened and browned, about 45 seconds. Add cognac; let stand until cognac warms slightly, about 10 seconds, then set skillet over high heat. Using chimney match, ignite cognac; shake skillet until flames subside, then simmer cognac until reduced to about 1 tablespoon, about 10 seconds. Add sauce base and mustard; simmer until slightly thickened and reduced to 1 cup, 2 to 3 minutes. Whisk in butter; off heat, add Worcestershire sauce, any accumulated juices from steaks, and 1 tablespoon chives. Adjust seasoning with salt and pepper.
Set steaks on individual dinner plates, spoon 2 tablespoons sauce over each steak, sprinkle with chives, and serve immediately, passing remaining sauce separately.