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1
Start with the gastrique. Add apple juice and honey to a saucepan over medium high heat. Let simmer alone for 5 minutes. Add apple cider vinegar and bring to a simmer again and add a pinch of salt. Let simmer for about 15 minutes, or until Brussels sprouts are done frying. It won't be a ton of liquid left, about 1/4 cup, but that's all you need.
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2
In a large, high sided frying pan or Dutch oven, add vegetable oil so it is between 1/4 - 1/2 inch deep. Heat over medium to medium high heat.
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3
Trim the Brussels sprouts. First remove all brown and wilted leaves, and trim the very bottom of the sprout. Don't remove the whole core. You want the leaves to stay attached.
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4
Test the oil by dropping in a loose leaf. The oil should sizzle around the sprouts, but not smack and shoot oil around your house. If it does, lower the heat a little bit and let it cool down. Drop Brussels sprouts, all cut side down, into the oil. Let sizzle in the oil on one side for about 5 minutes. Using tongs, turn over and let other side cook for about 4 minutes. The leaves should be golden but not black.
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5
Remove from heat to a mixing bowl, sprinkle with salt immediately and pour gastrique over everything. Mix and transfer to serving dish, leaving most of the liquid behind. Happy Thanksgiving!
