packed dried porcini or shiitake mushrooms, broken into chunky pieces
low-sodium soy sauce
packed dark brown sugar
hot prepared mustard
well-marbled porterhouse steaks, each about 800 and 4 centimeters thick
extra-virgin olive oil
kosher salt, divided
freshly ground black pepper
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 240 milliliters. 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 (230° to 290°C).
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.