Clean Brussels sprouts, cut stalks crosswise. Cut potatoes in half. Roast hazelnuts without fat. Pluck thyme.
Marinate potatoes with thyme and 2 tablespoons olive oil, season with salt and pepper.
Marinate Brussels sprouts with remaining olive oil, salt, pepper, chili flakes and agave syrup.
Bake potatoes and Brussels sprouts separately in oven at 180°C for about 20 minutes.
In the meantime, peel the carrots and cut into coarse sticks. Caramelize sugar in a pan, add carrots, deglaze with a little water. Simmer until the carrots still have a slight bite. Season to taste with salt.
Arrange potatoes and Brussels sprouts with the carrots on a plate. Garnish with pomegranate seeds and coarsely chopped hazelnuts.