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1
Put the yogurt in a paper towel-lined strainer set over a bowl, set aside to drain and thickened, about 60 minutes.
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2
Discard the watery liquid.
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3
Whisk the horseradish into the thickened yogurt.
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4
Meanwhile, heat 2 tablespoons of the olive oil in a medium skillet, over medium heat.
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5
Add the onions, 1 thyme sprig, and season with salt and pepper, to taste.
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6
Cook, covered, until the onions have wilted, about 10 to 15 minutes, (give them a stir every now and then with a wooden spoon to prevent them from sticking).
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7
Add the red wine, and simmer over high heat until most of the wine gets absorbed into the onions.
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8
Add the honey and red wine vinegar and simmer gently until the onions get jam-like, about, about 15 minutes.
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9
Preheat a stove top grill pan over medium-high heat.
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10
Whisk the remaining 2 tablespoons oil, garlic, and balsamic vinegar in a bowl.
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11
Strip and add the leaves from the remaining sprig of thyme.
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12
Coat the mushroom caps all over with the flavored olive oil.
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13
Grill the mushrooms, turning as needed, until tender but not mushy about 3 to 4 minutes per side.
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14
Season with the salt and pepper.
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15
Sandwich the mushroom between the buns, top with some of the onion jam, some lettuce, and a dollop of the horseradish cream.
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16
Serve warm.
