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1
To make the relish, heat the oil in a medium saute pan over medium-low heat.
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2
Add the onions and season with salt and pepper.
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3
Cover the pan with a lid and cook the onions, stirring occasionally, until soft, about 10 minutes.
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4
Increase the heat to medium-high and add the wine, vinegar, honey, and thyme and simmer, stirring occasionally, until the liquid evaporates and the mixture thickens to a jam-like consistency, 5 to 7 minutes.
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5
Transfer to a bowl, stir in the parsley, and let cool to room temperature.
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6
The relish can be made 2 days ahead and stored, covered, in the refrigerator.
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7
Bring to room temperature before using.
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8
Divide the meat into 4 equal portions (about 4 ounces each).
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9
Form each portion loosely into a 1/2-inch-thick burger and make a deep depression in the center with your thumb.
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10
Season both sides of each burger with salt and pepper.
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11
Heat the oil in a saute pan or griddle, preferably cast iron, over high heat until the oil begins to shimmer.
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12
Cook the burgers until slightly charred and cooked to medium, about 3 minutes per side.
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13
Butter 4 slices of the bread with 4 tablespoons of the butter.
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14
Turn the bread over (buttered side down) on a flat surface and divide half of the cheese over the top.
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15
Spoon half of the onion relish on top of the cheese, add the burgers, and then spoon on the remaining relish and cheese.
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16
Cover with the remaining 4 slices of bread and butter the tops with the remaining 4 tablespoons butter.
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17
Press down gently on the sandwiches.
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18
Wipe out the pan with paper towels and heat it over medium heat.
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19
Cook the melts until the bread is golden brown and crispy and the cheese has melted, about 1 1/2 minutes per side.
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20
Serve immediately, topped with pickled jalapenos, if desired.
