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Preheat a flat-top griddle, grill griddle or large skillet over medium-high to high heat.
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Place the ground bison in a large bowl. Add the diced onion, salt and black pepper.
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Cut four squares of parchment paper large enough to cover each portion of meat.
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Gently mix the bison mixture, then divide it into four equal portions. Roll each portion into a quarter-pound ball.
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Place the bison balls onto the hot cooking surface. Set a square of parchment over each ball and use a burger press or sturdy spatula to smash the meat into a thin patty.
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Remove and discard the parchment paper.
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Cook the burgers for 1–3 minutes per side, depending on thickness and preferred doneness.
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After flipping, place a slice of cheese over each burger and let it melt as the burgers finish cooking.
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Drizzle barbecue sauce over each burger.
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Transfer to toasted sesame seed buns and finish with your favorite burger toppings. Serve hot.