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Add enough canola oil to fill a medium heavy-bottomed skillet about ¼ of the way up. Heat the oil for five minutes over medium heat.
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Peel the shallots and then slice them into ¼-inch slices, width wise. Separate each ring of the shallot.
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Add the flour to a small bowl. Mix in a pinch of salt and pepper. Add buttermilk to a separate small mixing bowl. Drop the shallot rings into the buttermilk. Remove the shallots and toss them in the flour. Let the coated rings sit for a minute or two while the oil heats up.
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Drop all the rings into the hot oil and fry on each side for about three to five minutes until golden. Set crispy fried shallots on a paper towel to drain and cool
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Set the broiler to high.
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Form ground beef into seven small patties. Place patties on to a small baking sheet. Sprinkle the tops of each patty with salt, pepper, and Worcestershire sauce. Place under the broiler for three minutes, leaving the oven door cracked open.
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After three minutes, remove the pan of patties. Use a spatula to remove the patties from the sheet. Wipe off excess grease from the pan. Place the buns on the pan, cut sides facing up. Place each beef patty on the bottom half of each bun. Cover each patty with two to three little slices of cheese. Place the burgers back under the broiler for a minute or two, until the cheese melts.
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Spread a little spicy mustard on the top half of the bun if you desire. Top the burgers with a few crispy fried shallots and then cover with bun. Serve hot on the day you make it.