Heat the oven to 400 degrees F. 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.

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.

Put the finely chopped nuts, butter, lemon zest, thyme, honey, and 1/4 teaspoon salt in a small bowl and mix with a spatula until well combined. Set aside or refrigerate if not using right away.

Heat the oil in a 12-inch skillet over medium high heat. Add the Brussels sprouts and 1-1/2 teaspoon 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.

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.

Transfer the sprouts to a warm serving dish and garnish with the reserved hazelnuts.

Make Ahead: 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.