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Heat oil in a large skillet over medium heat and cook onion and salt for 20 minutes, stirring frequently, until onions very tender and become a deep caramel color.
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Form ground beef into 8 4-inch patties. On center of 4 patties, arrange 1½ tablespoons onions and 3 tablespoons Beemster. Place remaining patties on top and press to seal edges.
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Place burgers on hot grill and cook over medium heat turning once, until burgers are cooked to desired doneness.
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Top with bacon and remaining Beemster and grill until cheese is melted.
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Serve on buns with lettuce, tomato and any remaining caramelized onions.