In a small saucepan combine the sauce ingredients. Bring to a boil over high heat and then reduce the heat to low; partially cover the pan. Simmer the sauce gently to your desired thickness, 40 to 50 minutes (the sauce will be chunky and very aromatic). Let the sauce cool for 10 minutes. Set a fine-mesh strainer over a medium bowl and strain the sauce, pressing down on the solids to extract the juices. Discard the solids. (Yield: about 1 cup. May be kept in the refrigerator for up to 1 month.)
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Blot the steaks dry with paper towels. Brush both sides with the oil and allow the steaks to stand at room temperature for 30 minutes to 1 hour.
Prepare the grill for indirect cooking over high heat (450° to 550°F).
Brush the cooking grates clean. Season one side of each steak with ½ teaspoon salt and then place them, salted side down, over direct heat. Grill the steaks, with the lid closed, for 3 minutes. Season the top of the steaks evenly with the remaining 1 teaspoon salt, turn them over, close the lid, and cook for 3 minutes more.
Slide the steaks over indirect high heat and continue cooking, with the lid closed, until cooked to your desired doneness, 10 to 16 minutes for medium rare, turning once. Transfer the steaks to a rack placed on a platter (to keep them from resting in their own juices) and tent them loosely with foil. Let rest for 5 to 10 minutes. Season with the pepper.
Remove the two main pieces of steak from either side of the bone (the tenderloin and the strip steak). Cut each section across the grain into thick slices and serve on warm plates with the homemade steak sauce on the side.