Position a rack in the center of the oven and heat the oven to 400°F.
Pat the steak dry and season generously with salt and pepper. In an ovenproof heavy-duty 12-inch skillet (preferably cast iron), heat the oil over high heat until shimmering hot, about 2 minutes. Brown the steak on both sides, about 4 minutes total. Transfer the skillet to the oven and continue to cook until an instant-read thermometer inserted in the thickest part of the meat reads 135°F, about 5 minutes. Transfer the steak to a platter, cover loosely with foil, and let rest for 5 to 10 minutes.
Meanwhile, pour off the fat in the skillet (be careful of the hot handle). Set the skillet over medium heat, add the shallot, sherry, Cognac, and Worcestershire sauce. Simmer, stirring and scraping the bottom of the pan with a wooden spatula to release any browned bits, until the sauce is reduced by half, 2 to 3 minutes. Lower the heat to low, add the chicken broth, butter, chives, and parsley and whisk, swirling the pan occasionally, to emulsify the butter; the sauce should look creamy. Remove from the heat, whisk in the lemon juice and season to taste with salt, pepper, and more lemon juice.
Cut the steak in half with the grain, then slice the meat on the diagonal across the grain into 1/8-inch slices. Serve with the sauce.