Step 1Heat the oven to 300 degrees. Bring a large saucepan of water to a boil, and add the pecans. Boil until the nuts are softened, about 5 minutes. Strain the nuts, discarding the water.
Step 2In a medium bowl, toss the nuts with the sugar, honey and a pinch of salt. Place on a parchment-lined rimmed baking sheet and cook until the nuts are dried and toasted, 45 minutes to an hour. Toss the nuts after 25 minutes, and then check every 5 to 10 minutes. Remove and set aside to cool. This makes more candied pecans than are needed for the remainder of the recipe; the nuts will keep for weeks, sealed in a container in a cool, dry place.
Step 1Adjust the oven to 400 degrees. In a bowl, toss the sprouts with the olive oil, salt and pepper, then spread them out on a rimmed baking sheet. Roast the sprouts until the edges start to crisp, 25 to 30 minutes, tossing halfway. Remove from the oven and set aside to cool. The Brussels sprouts can be made up to 3 days in advance; cover and refrigerate until needed.
Step 1In a measuring cup or deep bowl, combine the mustard, shallots, honey and vinegar. With an immersion blender running, slowly drizzle in the olive oil to blend. Season with a pinch each of salt and pepper, or to taste. This makes about three-fourths cup dressing, more than is needed for the remainder of the recipe; the dressing will keep up to 1 week, covered and refrigerated.
Step 1In a large sauté pan heated over high heat, add the butter, oil and sprouts (depending on the size of your pan, this may need to be done in batches to prevent crowding). Sauté the sprouts to warm through, 3 to 5 minutes. Add the pecan halves and drizzle over the Dijon dressing, tossing to coat. Remove from heat.
Step 2Divide the salad among four plates and top each with crumbled goat cheese. Serve immediately.