Take the steak out of the refrigerator about half an hour before cooking it to bring it to room temperature.
In a large skillet, heat 1 tablespoon clarified butter; add the onions and cook, stirring occasionally until the onions begin to caramelize, about 8-10 minutes.
Add 1½ tablespoons balsamic vinegar, season to taste, and continue cooking for 1-2 minutes. Set aside while you cook the steak.
Pat the steak dry with paper kitchen towels, brush with some clarified butter, and season to taste.
Heat a medium cast-iron skillet and add the steak. Sear it for about 1 minute per side, then the remaining clarified butter, garlic, thyme, and balsamic vinegar. Cook for another minute or so per side, flipping once until it forms a nice brown crust.
Once it has cooked to the desired doneness, transfer to a plate and tent with aluminum foil. Let it rest for about 5-6 minutes then cut it and serve topped with the caramelized onions.
