Tie the tail (thin end), back so that the loin is the same thickness all the way down, this will help it cook evenly. Use your favorite steak seasoning on the beef loin (see KC Strip Surf n' Turf for my favorite seasoning and how to dry brine the loin). Let set in fridge for at least two hours.
Heat your grill to medium/high heat. Brown the beef loin on all sides. You are NOT wanting to cook it per say, you are wanting to build a crust on all sides. When you have developed a nice color, pull the loin off and set aside.
Slice your onions and peel the garlic (leave whole cloves, minced garlic will burn).
Melt the butter in a large cast iron skillet on medium/high heat (I do this on the grill, or you can do it on a stovetop, or the Blackstone), add the onions, garlic, thyme and beef loin.
Turn the beef loin every few minutes to keep it coated in the butter. Cook the loin until it is your desired doneness. I pull it at 120degrees for medium rare, it WILL rise in the cast iron skillet.
The butter, garlic, and onions will be sizzling, and it makes a great presentation to take the entire skillet to the table. It will be sizzling like fajitas at a Mexican restaurant!
Slice into medallion sized slices and serve topped with the onion mixture.
