In a large glass baking dish combine the marinade ingredients. Whisk to dissolve the tomato paste. Submerge the steaks in the marinade. Cover and refrigerate for 2 to 4 hours.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Lift the steaks from the dish and pat dry with paper towels. Discard the marinade. Lightly brush the steaks with oil and season evenly with salt and pepper. Allow to stand at room temperature for 15 to 30 minutes before grilling. Meanwhile, make the sauce.
In a medium saucepan over medium heat, melt the butter. Add the shallot and cook until tender, about 2 minutes, stirring often. Mix in the sour cream and cheese and cook until the sauce begins to simmer and the cheese has melted, about 3 minutes, stirring occasionally. Remove from the heat, add ¼ teaspoon pepper, and cover to keep warm.
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 for 3 to 5 minutes. Serve warm with the sauce. Garnish with chives, if desired.
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