Blend together butter, thyme and mustard; season with salt and pepper. Place butter on waxed paper or parchment; roll into a log about 1-1½" thick. Wrap in plastic and refrigerate until firm.
Trim steaks of any exterior fat. (Leaving the fat on will result in a lot of smoke in your broiler.) Pat steaks dry with paper towels. Season both sides with salt and pepper. Do not use your oven's broiling pan; it's too shallow. Pour 2 cups of salt into a 3" deep disposable roasting pan, then place a cooling rack over the pan. The salt will catch any drips and prevent them from flaring or smoking. Place steaks on the rack.
Place steaks in a preheated 375°F oven for 6-8 minutes to bring them up to temperature. Turn steaks over and pat dry again with paper towels. Let rest 10 minutes while preheating broiler.
Place roasting pan in broiler, positioned so steaks are 1-1½" from the heating element. Broil 3 minutes, then turn steaks over and broil another 3 minutes. Continue flipping the steaks every 3 minutes until center registers 125-130°F (for medium-rare), 6-16 minutes. Transfer to a serving platter and top each steak with one quarter of the compound butter. Tent with foil and let rest about 5 minutes before serving.
Note: timing depends on how strong your broiler is. Place a slice of plain white sandwich bread under your broiler, about 3" from the heat. If your bread is toasted in under 30 seconds, you have a very strong broiler and should use the shortest times. If longer than 2 minutes, your broiler is very weak, and use the longest cooking times.
Note: for 1" steaks, prebake 6 minutes and flip every 2 minutes. For 1½" steaks, prebake 8 minutes and flip every 3 minutes. For 2" steaks, prebake 10 minutes and flip every 4 minutes.