Preheat grill to medium heat.
Over medium heat melt butter in a heavy bottomed saute pan. Add the chopped shrimp, and salt and pepper, to taste and saute for 3 minutes. Add garlic and shallots and continue to saute until shrimp is bright pink and opaque. Stir in the white wine and cook until dissolved. Season with cayenne pepper. Remove the shrimp mixture to a glass bowl and let cool. Once cooled, add 2 sticks of butter and fold together to combine.
Season the steaks with salt and black pepper on both sides.
Grill the steaks until cooked to desired doneness, about 3 to 4 minutes per side, for medium-rare. Transfer the steaks to serving plates and let rest for a few minutes.
Serve the steaks with a large dollop of shrimp butter on top and sprinkled with chives.