Preheat oven to 425°F (220°C). Toss Brussels sprouts with oil; season with salt and pepper. Roast in centre of preheated oven on a baking sheet lined with lightly greased aluminum foil, about 30 minutes.
Meanwhile, heat butter in a small saucepan with a light-coloured bottom (so you can see the colour change) over medium heat. As the butter melts, it will begin to foam and turn to a toasted brown colour, about 2 or 3 minutes. Once butter smells nutty, remove pan from heat. Strain butter with a cheesecloth or remove milk solids with a spoon; set aside.
In another saucepan, add vinegar, seeds from vanilla bean, the residual vanilla bean and sugar. Heat over medium high heat just until all of the sugar has dissolved, about 1 or 2 minutes. Turn off heat, cover with a lid and let steep, about 30 minutes.
After 30 minutes in the oven, top Brussels sprouts with hazelnuts and return pan to oven to cook for another 10 to 15 minutes, or until vegetables are tender. While roasting, remove vanilla bean from vinegar and whisk butter into vinegar. Season with salt and pepper to taste. Transfer vegetables to serving dish when finished and drizzle with vanilla bean brown butter glaze.
While they are roasting, remove the vanilla bean from the vinegar and whisk in the butter. Season with salt and pepper to taste. Transfer vegetables to serving dish when finished and drizzle with the vanilla vinaigrette.