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Melt the butter and whisk in the hot sauce.
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Mix the blue cheese and garlic in a small bowl.
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Using your hands, gently mix the ground beef, celery seed, onion and 1/4 cup hot sauce mixture in a medium bowl until blended. Form into 12 patties, using a light touch; the patties should be about 4 1/2 inches in diameter and no more than 1/2 inch thick.
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Spoon about 2 teaspoons of the cheese-garlic mixture in the center of 6 patties, then top with remaining patties and press together, sealing edges.
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Cover and refrigerate until ready to grill. (Even if you aren't making these ahead of time, I think they hold together better after a little chill time).
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Heat grill to medium and oil grate.
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Grill burgers about 4-5 minutes on each side, or until cooked to taste. Brush with the remaining hot sauce mixture during last 2 minutes of cooking. Toast buns if you like.