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1
To make the sauce: Place the mayonnaise, sour cream, basil, scallion, garlic, Worcestershire sauce, salt, and pepper in the bowl of a food processor and puree until creamy and pale green.
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2
Transfer to a small bowl, cover with plastic wrap, and refrigerate until you are ready to use it.
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3
To make the burgers: Heat a charcoal or gas grill to medium-high.
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4
Divide the ground beef into 4 equal pieces and gently form into patties.
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5
Use your thumb to make a small indentation in the middle of each burger (this is so the burger grills flat and doesn't contract and puff up on the grill).
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6
Brush both sides of the burgers with the oil and then season with salt and pepper.
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7
Place the burgers on the grill and cook until they have grill marks, about 4 minutes.
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8
Flip the burgers, cook 2 minutes longer, and then top each with about 1 tablespoon of the mozzarella.
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9
Cook the burgers 2 more minutes for medium-rare doneness and remove from the grill.
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10
Place the buns on the grill, cut side down, and lightly toast, 30 seconds to 1 minute.
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11
Set a burger on each bottom bun half.
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12
Top with a salted tomato slice.
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13
Spread 1 tablespoon of the garlic-herb sauce on the top bun half, sprinkle with Parmesan, cover the burger, and serve with more sauce on the side for dipping.