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1
Make the butter
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2
Heat the oven to 400u00b0F. Put the hazelnuts on a small rimmed baking sheet. Roast in the oven until they are a deep golden-brown (the skins will be visibly splitting), 5 to 6 minutes. Wrap the nuts in a clean kitchen towel, cool for a couple of minutes, and then take the skins off by rubbing the nuts together in the kitchen towel while still warm. Don't worry about getting all of the skins off.
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3
Let the nuts cool for about 10 minutes. Finely chop 1/4 cup of the nuts in a small food processor. The nuts should be very finely ground, but not so much that they turn into nut butter. Coarsely chop the remaining nuts and set aside for a garnish.
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4
Put the finely chopped nuts, butter, lemon zest, thyme, honey, and 1/4 tsp. salt in a small bowl and mix with a spatula until well combined. Set aside or refrigerate if not using right away.
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5
Cook the brussels sprouts
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6
Heat the oil in a 12-inch skillet over medium high heat. Add the Brussels sprouts and 1-1/2 tsp. salt and stir well. Reduce the heat to medium and cook, stirring occasionally and then more frequently as the sprouts begin to brown, until all of the sprouts are golden-brown on most sides and have lost their raw color (they will still feel firm), 15 to 18 minutes.
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7
Add the broth and immediately cover the pan. Cook until the broth has reduced to a few tablespoons, about 2 minutes. Uncover, raise the heat to high, and boil off most of the remaining liquid, 1 to 2 minutes. Take the pan off the heat and add the hazelnut butter in spoonfuls; toss well. Season to taste with salt.
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8
Transfer the sprouts to a warm serving dish and garnish with the reserved hazelnuts.
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9
Make Ahead Tips
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10
You can trim and quarter the Brussels sprouts several hours before cooking. The butter can be made and refrigerated (tightly wrapped) 2 days ahead. Store the extra nuts for garnish at room temperature.