Make sure that your meat is at room temperature.
Heat an oven-proof sauté pan to high on the stove and set the temperature of the oven to 200˚C (395˚F).
Do not season the meat unless you want to steam it (and trust me, you don’t).
Add the butter and a dash of olive oil to the pan.
Pat dry the meat before placing it carefully in the hot pan. Add a bunch of thyme to the pan.
You want a good dark crusty exterior for the meat, so don’t move or turn it until you get it; this should take around 3 minutes per side, or 5 if you have a crappy electric stovetop.
Once both sides are cooked, I like to set the other bunch of thyme on fire, get it really smoking, add it to the pan, and partially cover the pan. This should take a couple of minutes to get a decent aroma through the meat.
Place the meat in the oven; it should be around 10 minutes to get to rare to medium-rare.
Remove the meat from the oven and rest covered in a warm place.
Traditionally, côte de bœuf is sliced at the table, seasoned and served.
The next day if you haven’t finished the beef, you’re going to have the best beef and mustard sandwiches of your life!