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1
Start the coals or heat a gas grill for medium-high direct cooking. Make sure the grates are clean. Cut at least ten 8-inch pieces of kitchen twine.
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2
With a very sharp knife, slice the steak lengthwise into two pieces. With a meat mallet, rolling pin, or the bottom of a cast-iron skillet, pound the two thin steaks evenly to no more than 1/2-inch thick. Pat them dry with paper towels and sprinkle with salt and pepper on both sides.
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3
Combine the cheese, oregano, and garlic in a small bowl. Divide the mixture between the steaks and spread it out almost to the edges. Roll the steaks up so that the grain of the meat runs the length of the roll, so you'll be slicing them across the grain. Tie the steaks closed with the twine every 2 inches or so. (You can prepare the recipe to this point up to several hours in advance and refrigerate.)
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4
Put the stuffed steaks on the grill directly over the fire. Close the lid and cook, turning the rolls every 2 to 3 minutes for even browning, until 5 to 10u00b0F shy of the desired doneness; start checking them with an instant-read thermometer after 10 minutes. Depending on the thickness of the rolls, they should take 15 to 20 minutes total for medium-rare.
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5
Transfer to a cutting board and let rest 5 to 10 minutes, checking the internal temperature. (Or nick with a small knife and peek inside.) Cut the rolls into 1-inch slices, transfer them spiral side up to a platter, pour over any accumulated juices, and serve.
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6
Substitute shredded mozzarella for the queso asadero and omit the oregano. Top the cheese with a layer of fresh basil leaves before rolling; you'll need 1 cup or more.
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7
Substitute Parmesan cheese for the queso asadero and 2 tablespoons chopped rosemary for the oregano. In Step 3, layer 4 ounces thinly sliced prosciutto over the cheese before rolling.
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8
Replace the cheese, oregano, and garlic with 8 ounces goat cheese, 1 tablespoon minced garlic, the grated zest of 1 lemon, 1 tablespoon fresh lemon juice (or more to taste), and lots of black pepper, mashed together in a small bowl. Spread the mixture over one side of each of the steaks. Layer 2 cups roughly chopped watercress or arugula over the top before rolling.
