Using a sharp knife cut off a small amount of the core as shown in the picture. Only discard outside leaves if they don't look fresh. Cut each sprout in half along the core.
Wash the Brussels sprouts and any loose leaves in a large colander with cold, running water. Drain well and put the sprouts into a large baking pan, like a Pyrex glass pan, a roasting pan, or baking sheet.
Peel the tangerine, separate the segments, and cut each one in half. Remove any seeds. Add the tangerine and the juice on the cutting board to the spouts.
Add the remaining ingredients to the pan and toss everything together to evenly distribute all of the ingredients.
Place the pan in the oven (middle or top rack) and cook for 40-60 minutes.
Stir the Brussels spouts every 15 minutes. Add a tablespoon or more of water if the liquid evaporates to prevent sticking or burning. Total cooking time will depend on the size of the spouts and how well you want them cooked. They are cooked when you can easily insert a fork into the sprout. Avoid over cooking as this will cause them to turn bitter.