After the steak has marinated overnight for at least 2 days, remove the cheesecloth from around the steaks. The steaks should be well-seasoned from the salt and the miso. Allow the steaks to sit out and come to room temperature to help with even cooking for at least 10 minutes.
Preheat the grill or a heavy bottom cast-iron skillet over medium-high heat. Also, have your oven preheated to 350F.
Add in 3 tablespoons of canola oil to the hot pan. The oil should be smoking before adding the steaks. Carefully add in the steaks while tilting the oil to one side to prevent the hot oil from splattering on you. Sear on high heat for 4 minutes on each side. Add in 1 tablespoon of butter to the pan and continue to cook the steak for 1 more minute on each side. Once there is a good color on both sides of the steak, remove the steak from the pan and place on a small baking sheet. Place the steak in the oven and cook for another 2–3 minutes to the desired internal temperature. Test the temperature of the steaks in the center with an instant-read thermometer. For medium-rare, pull the steak at 110F. For medium, pull at 118F–120F. For more done, pull at 135F or above.
The same method can be used for the grill, except you would rub the steak with a small amount of the oil before placing it on the grill. Cook over high heat to get a good color, then finish in the oven if needed.
Once the steak is cooked to the desired temperature, place it on a small tray to allow it to rest before slicing. The steak should rest for at least 5 minutes.
Once rested, reheat the carrots in the oven. Slice the ribeye against the grain of the meat and serve on plates with the warm carrots.