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In a large bowl mix together by hand the ground beef and the rest of the teriyaki sauce until well incorporated.
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Cover half of the grill grate with aluminium foil.
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Place the burgers on the foil and cook for 6-8 minutes per side.
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Once the burgers are cooked top with a slice of provolone cheese.
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While the cheese is melting, place 4 pineapple rings on the grill grate.
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Cook the pineapple about 1 minute per side, until they are charred.
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Place a pineapple ring on top of each burger.
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Slather the hamburg roll with the teriyaki mayonnaise and enjoy!