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Pre-heat air fryer and/or oven to 400ºF.
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Toss the Brussels sprouts with a little olive oil and season with salt and freshly ground black pepper. Transfer to a sheet pan and bake in the oven for 30 minutes. Shake or stir the Brussels sprouts halfway through the cooking time.
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Place the diced bacon into the air-fryer basket and add a little water to the drawer below to catch the grease. Air-fry for 10 minutes, tossing or stirring a few times during the cooking process. Add the shallots and air-fry for another 10 to 15 minutes, until the bacon just starts to brown and the shallots are soft. Season with freshly ground black pepper and drain on paper towels.
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While the Brussels sprouts are roasting and the bacon is air-frying, melt the butter in a medium saucepan. Add the flour and whisk until combined. Slowly pour in the heavy cream and milk and whisk until the mixture is smooth and the sauce starts to thicken, about 3 to 5 minutes.
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Add the horseradish, salt, and nutmeg, and stir in the fresh thyme.
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Transfer the Brussels sprouts from the oven into a 9-inch x 13-inch baking dish. Pour the horseradish cream sauce evenly over Brussels sprouts. Sprinkle the bacon and shallots over the top.
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Bake at 350ºF oven for 30 minutes. Serve hot.