Remove the steaks from the refrigerator 30 minutes before grilling and let sit on a kitchen counter, loosely covered.
Heat the grill to high. Set a cast-iron skillet large enough to hold both steaks on one side of the grill. Brush the steaks with canola oil and season very liberally with salt and pepper. Grill until well charred on the first side, 2 to 3 minutes; flip and grill until well charred on the second side, another 2 to 3 minutes. (The steaks should still be raw at the center at this point.) Transfer to a cutting board.
Slice the steaks across the grain about 1 1/2-inches thick; don't separate the slices. Keeping the steak slices together, transfer the steaks to the skillet and top with the butter. Cover the grill and cook the steaks for 5 minutes for medium rare. Transfer the skillet to a trivet.
Arrange the steak slices on a platter so that the interior of the slices is facing up. Top each slice with some blue cheese. Pour the hot brown butter from the skillet over the steak. Serve immediately.