Preheat the oven to 400°F. Toss the Brussels sprouts with one tablespoon of the oil and spread them out on a rimmed baking sheet. Sprinkle with salt. Roast for 20 to 25 minutes until the Brussels sprouts are fairly tender and browned in spots. Let cool slightly, on the baking sheet, for about 10 minutes.
While the Brussels sprouts are cooking, make the dressing. In a food processor place the remaining 3 tablespoons olive oil, lemon juice, anchovies, garlic, mustard, scallions, parsley and pepper and process until pureed.
Drizzle the Brussels sprouts with about half of the dressing and toss to coat. Add more dressing if you like. Transfer the Brussels sprouts to a serving dish and serve warm, with the rest of the dressing on the side.
You can make the dressing ahead of time, and then just simply roast the Brussels sprouts before the meal, toss them with the vinaigrette and serve them warm or even room temperature. I’m not the biggest fan of reheating Brussels sprouts, and would prefer to just serve them at room temperature if they cool down. But you can – don’t mind me.Don’t oversalt the Brussels sprouts because the anchovies add salt to the dressing. You can always add a pinch of salt to the final tossed salad if you want.