In a large bowl combine the marinade ingredients, whisking in the oil until blended. Divide the marinade, pouring 3 cups into a non-reactive baking dish and leaving the other 1 cup in the bowl. Add the baking soda to the marinade in the baking dish for a tenderizing effect (the mixture may fizz a little).
Put the steaks into the dish with the marinade and turn to completely coat the steaks. Let marinate at room temperature for 30 minutes, turning once.
Place the sliced onions in the bowl with the marinade and gently stir to coat them evenly. Set aside and let them marinate alongside the steaks.
In a medium bowl mix the sour cream and horseradish. Stir in the thyme, and season to taste with salt and pepper. Cover and refrigerate until ready to use.
Prepare the grill for direct cooking over high heat on one side of the grill and medium heat on the other. Brush the cooking grates clean. Remove the steaks from the dish, allowing most of the marinade to drip back into the dish. Discard the marinade. 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. While the steaks are grilling, carefully remove the onions from the marinade, keeping the bowl of marinade close by, and grill the onions over direct medium heat for 6 to 8 minutes, turning once. Remove the onions from the grill and plunge back into the bowl of marinade. Toss to coat and let the onions soak up the marinade while the steaks rest for 3 to 5 minutes. Slice and toast the cut sides of the rolls over direct medium heat, about 1 minute.
To assemble the sandwiches, slice the steaks on the bias into thin strips. Pile the bottom of a French roll with onions and layer with strips of steak. Top with horseradish sauce and watercress.
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