Using an electric mixer, whip room-temperature butter on medium speed for 2 minutes, then add the garlic, shallot, red wine and blue cheese and mix just to blend. Season butter to taste with salt and pepper.
Either put butter in small bowl or on wax paper and roll it into a log. Place butter into refrigerator until you are ready for it. You may store butter covered in the refrigerator for 3 days or freeze it for 3 months.
Preheat grill to medium-high heat.
Brush each steak all over with oil and season to taste with salt and pepper. Before putting the steaks on grill, let them sit at room temperature for 10 minutes.
Cook steaks on grill to desired doneness or until meat reaches an internal temperature of 160°F on a meat thermometer for medium doneness.
When steak is ready, remove from grill and top with some butter while still very hot.