Move the steaks to the hot zone and continue cooking.
Flip the steaks after 2-3 minutes, checking regularly with your Thermapen.
When your steaks are 5° below your target temp, pull them from the grill.
Tent the steaks and let them rest 5 minutes.
For the butter
Prepare flavorings.
Mix the butter and flavorings well in a mixer.
Press out into a rough cylinder.
Roll in parchment paper, forming into a better cylinder.
Twist ends of the paper to finish the form.
Store in refrigerator or, if for later use, the freezer.
Bring it all together
If your butter is cold and firm, place a slice of it on each steak as soon as they come off the grill. If the butter is still quite soft from beating, you can add it right before serving. Either way, it will melt and spread its flavors over the surface of the steak, pooling at its base to create a sauce as fine as any chef could ever hope to make.