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1
Melt the butter in a small saucepan over medium heat.
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2
Whisk in the flour and cook for 1 minute.
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3
Add the milk, increase the heat to high and cook, whisking constantly, until slightly thickened, about 5 minutes.
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4
Remove from the heat and whisk in the cheese until melted; add the Parmesan and season with salt and pepper, to taste.
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5
Keep warm.
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6
For the relish:
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7
Combine all ingredients in a bowl and season with salt and pepper, to taste.
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8
For the pickled red onions:
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9
Bring vinegar, water, sugar and salt to a boil in a small saucepan over medium heat.
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10
Remove from the heat and let cool for 10 minutes.
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11
Put the onions in a medium bowl, pour the vinegar over, cover and refrigerate for at least 4 hours and up to 48 hours before serving.
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12
For the burgers:
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13
Heat a griddle or large saute pan over high heat.
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14
Add the oil and let it heat until it begins to shimmer.
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15
Shape the ground beef with your hands into 4 round patties about 1 1/2 inches thick and season each burger on both sides with salt and pepper, to taste.
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16
Cook the burgers until golden brown on both sides and cooked to medium, about 8 minutes.
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17
Put the burgers on the buns and top each with a few tablespoons of the queso sauce, relish, onions and chips.
