Preheat the oven to 190ºC. Spread the pecans in a shallow baking pan and roast in the oven until fragrant, 10 to 12 minutes, stirring occasionally. Let cool completely. Finely chop the pecans.
In a medium bowl fold all the butter ingredients, including ⅛ teaspoon black pepper, with a rubber spatula until incorporated. Place the mixture on a piece of plastic wrap and form into a log. Chill until firm enough to slice, 20 minutes in the freezer or 45 minutes in the refrigerator.
Prepare the grill for indirect cooking over medium heat (180° to 230°C).
In a large bowl whisk 2 tablespoons oil with the granulated garlic, ¾ teaspoon salt, and ¼ teaspoon pepper. Add the sweet potatoes and turn to coat evenly. Grill the potatoes, cut side down, over indirect medium heat, with the lid closed, until they start to soften, about 30 minutes, turning once.
Adjust the grill to direct low heat (120° to180°C) on one side, and direct high heat (180° to 230°C) on the other side. Brush the sweet potatoes with oil, and then grill, cut side up, over direct low heat, with the lid closed, until fork tender, browned, and crisp on the top, 20 to 25 minutes.
Brush the steaks with 1 tablespoon oil and season evenly with ¾ teaspoon salt, and ½ teaspoon pepper. Grill the steaks over direct high heat, with the lid closed, until cooked to your desired doneness, 6 to 8 minutes for medium rare, turning once.
Remove the steaks from the grill and let rest for 5 minutes. Top each steak and the sweet potatoes with a slice or two of butter. Serve warm.