Remove the steaks from refrigerator 30 minutes prior to cooking. Season liberally with kosher or sea salt on both sides. Allow steaks to come to room temperature. Pat surface of steaks dry with a paper towel prior to searing.
Heat grill to high heat or approximately 450F. Once grill is up to temperature, place skillet in grill and allow skillet to heat thoroughly. If cooking indoors, pre-heat skillet to medium-high heat. Add oil for searing once skillet is hot and carefully place steaks in skillet and sear for a couple minutes or two until nicely browned on both sides. Only flip the steak once. If the pan does not sizzle nicely when you put the steak in, it is not hot enough. Remove steaks from skillet. You will use that skillet for the sauce.
If finishing steaks in the oven, place steaks in a pre-heated 375°F oven and cook until approximately 10-15 minutes or until 5°F shy of desired finished temperature. Finished temperature for med-rare 130-135°F, medium 140-145°F, med-well 150-155°F, well done 160°F. For example, if you desire a med-rare steak pull at 130F because the temperature will rise during the 5 minute rest period. If cooking steaks on the grill, finish cooking the steaks in the skillet first, then set meat aside to rest (tent loosely with foil) and keep warm while using the same skillet to make sauce.
In the same skillet you seared the steaks add butter and sauté celery first as that takes the longest to cook. Cook until it is tender. Add peppers and sauté until tender. Add mushrooms and cook until lightly browned and most of the water has evaporated. Add shallots and garlic then cook until transluecent approximately 1 minute. Add sherry to skillet to deglaze pan. Stir to scrape off brown bits on bottom of skillet into sauce. Add chicken stock. Continue to cook for 2-3 minutes.
Make cornstarch slurry to thicken sauce. Miix 1 tbsp cornstarch with 1 tbsp of COLD water until thoroughly incorporated. Push vegetables in skillet to one side and add one-half of slurry to liquid and whisk . Stir into rest of skillet ingredients. Cook for 1 minute until sauce thickens. If sauce is not thick enough, add a bit of the remaining slurry. You want the sauce to coat the back of a spoon, not be thick like gravy.
Place the steak on a plate and serve with sauce on top. Serve immediately.