Let steaks stand at room temperature 15 to 20 minutes. Rub steaks evenly with steak seasoning (I use McCormick Grill Mates Montreal Steak Seasoning).
Grill, covered with grill lid, over medium heat (300 to 350) for 2 1/2 minutes. Using tongs, turn each steak at a 60-degree angle, and grill 2 1/2 minutes more. Flip steaks, and grill 2 1/2 minutes. Turn steaks at a 60-degree angle, and grill 2 1/2 more minutes (medium-rare) or to desired degree of doneness.
Remove steaks from grill, and brush evenly with butter. Let stand 5 minutes.
(If you want rare steaks, adjust the time to 2 minutes in the above directions; for medium doneness, grill 4 minutes each turn; and for medium-well, allow about 5 minutes each turn).