Let the beef tenderloin filets sit at room temperature for about 30 minutes before cooking.
Meanwhile, bring salted water to a boil in a medium saucepan and fill a medium bowl with ice water. Add the bok choy to the boiling water and cook until slightly tender, about 1 minute. Transfer to the ice water until cool, then drain, quarter lengthwise and set aside.
Heat 1 tablespoon canola oil in a medium saute pan over medium-high heat. Add the mushrooms and shallots, then sprinkle with salt and pepper and let cook, stirring occasionally, until the mushrooms brown and the shallots begin to soften, about 5 minutes. Add the chicken stock, coconut yogurt, miso, mustard and sesame oil and stir together. Let cook, stirring occasionally, until the liquid reduces by about half, about 5 minutes. Set aside.
Sprinkle filets on both sides with salt and pepper. Heat the remaining tablespoon canola oil in a medium heavy-bottomed saute pan over medium-high heat. Add the steaks and let sear, without moving, until browned, about 2 minutes. Turn the filets over and add the butter, thyme and garlic to the pan. Once the butter melts, begin basting the steaks with the butter until browned on the second side, 2 to 3 minutes more for medium-rare. Remove the steaks from the pan, pour over the pan sauce and let rest.
Add the bok choy to the same pan and let brown, 1 to 2 minutes. Add the steak and any accumulated pan juices back in, along with the vinegar. Take the pan off the heat and add the tequila, then tilt the pan into the flame or use a match to carefully ignite the pan. Let the fire subside, then remove the pan from the heat. Divide the bok choy between 2 plates. Top each with a steak, then spoon the mushroom and sauce mixture over both steaks. Garnish with cilantro and serve.