In a small bowl combine the butter ingredients. Scoop the mixture out of the bowl onto a sheet of parchment or waxed paper. Loosely shape the mixture into a log about 1 inch in diameter. Roll the log in the paper and twist the ends in opposite directions to form an even cylinder. Refrigerate for at least 1 hour, or until the butter is chilled.
Lightly brush the steaks on both sides with oil and season evenly with salt and pepper. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling. In a large bowl of water, submerge the broccolini for 20 to 30 minutes so that they absorb water. This will help them steam a little on the grill.
Prepare the grill for direct and indirect cooking over high heat (450° to 550°F).
Pour off the water from the bowl of broccolini. Lightly drizzle some oil over the broccolini and season with salt and the red pepper flakes. Toss to coat evenly.
Brush the cooking grates clean. Grill the steaks over direct high heat, with the lid closed as much as possible, until cooked to your desired doneness, 6 to 8 minutes for medium rare, turning once or twice (if flare-ups occur, move the steaks temporarily over indirect heat). Remove from the grill and let rest while you grill the broccolini.
Using tongs, lift the broccolini and allow any excess oil to drip back into the bowl. Grill the broccolini over direct high heat, with the lid closed as much as possible, until lightly charred, 3 to 4 minutes, turning occasionally. Finish cooking over indirect high heat for 2 to 3 minutes.
Cut four ½-inch-thick pieces of butter and place one in the center of each steak. Serve warm with the broccolini.