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1
In a medium-size saute pan or skillet, melt the butter over medium heat.
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2
Add the onion, cover, reduce the heat to low, and cook, stirring occasionally, for 15 minutes.
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3
Remove cover, and continue to cook the onion over low heat until very soft and golden, about 45 minutes longer, stirring to keep onions from sticking to pan.
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4
Start up grill or preheat a broiler.
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5
While onions are cooking and after grill is lit, combine ground beef, Worcestershire sauce, and salt and pepper to taste in a large bowl.
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6
Handling the meat as little as possible to avoid compacting it, mix ingredients together well.
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7
Divide the mixture into 8 equal portions, and form into thin, round patties to fit the bread slices.
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8
Cut the cheese into 4 pieces a little smaller that the patties.
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9
Place a piece of cheese on 4 of the patties, cover with the remaining patties, and press edges together to seal and encase the cheese.
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10
When grill is ready, brush the grill rack or broiler rack with vegetable oil.
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11
Place the patties on the grill rack or under the broiler and cook until browned, about 4 minutes.
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12
With a wide spatula, turn the patties and cook until done to preference, about 4 minutes longer for medium rare.
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13
During the last few minutes of cooking, place the bread slices on the outer edges of the grill to toast lightly or prepare in toaster.
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14
Top 4 slices of the bread with the patties, pile on the onion, and cover.
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15
with the remaining bread slices.
