Heat oven to 425°F. Season room temperature ribeyes liberally on all sides with Kosher salt and black pepper. Let stand 20 minutes while you slice the mushrooms and the shallots.
Dip a clean paper towel in 2 tablespoons of canola oil and wipe the entire inside surface of a large cast iron skillet. Place the skillet on the stove. Add 1 tablespoon of oil to the center of the skillet over medium high heat. Wait for the oil to shimmer. Using kitchen tongs and a clean piece of paper toweling, wipe the majority of the oil from the pan. *See Notes Below
Add the steaks to the hot pan and do not move them. Sear 1 to 2 minutes per side. Then transfer the pan to the oven and cook for an additional 5 to 7 minutes or until an instant read thermometer reads 145°F for medium.
Carefully remove the skillet from the oven using oven mitts and transfer the steaks to a cutting board or platter. Cover immediately with heavy gauge aluminum foil to keep warm. Rest the steaks for 10 minutes while you prepare the shitake and shallot pan sauce.
In the cast iron skillet over medium heat, cook the shiitakes and the shallot, stirring until the shiitakes begin to brown. Stir in butter and then the garlic. Cook 2 minutes. Add sherry, Teriyaki sauce, beef broth, and red pepper flakes and cook 2 minutes more. Stir in heavy cream and cook over medium low heat 3 to 5 minutes. Stir chives into the sauce. Stir any accumulated juices from the meat into the sauce.
To serve, either plate steaks or carve thin and add to a platter. Spoon the shiitake shallot pan sauce over the ribeyes.