Combine vinegar, sugar, thyme sprigs, and 1/4 cup water in a small saucepan. Bring to a boil. Remove from heat and let sit 5 minutes. Combine sliced shallots and 3 tablespoons oil in a bowl. Pour hot vinegar mixture over shallots and let sit at room temperature 2 hours or refrigerate up to 48 hours. Drain; discard thyme.  Preheat oven to 425°F. Toss together Brussels sprouts, garlic, chopped shallot, and remaining 3 tablespoons oil in a roasting pan. Season with salt and pepper. Roast until Brussels sprouts begin to brown, 12 to 15 minutes.  Melt butter in a small sauce-pan over medium heat. Cook, stirring occasionally, until light golden brown, 1 to 2 minutes. Add hazelnuts and toss to coat. Season with salt.  Serve Brussels sprouts topped with pickled shallots and hazelnuts.