Prepare the leeks by removing the dark green tops so that you are left with the white and light green parts. Slice the leeks in half lengthwise, keeping the roots intact, so that you have 8 long pieces. Place them in a bowl, baking dish, or rectangular container, and cover with water. Swish the leeks in the water, gently peeling apart their layers if needed, to remove dirt. Remove the leeks from the water and pat dry.
In a large skillet, preferably a cast iron one, heat the butter over medium heat. Place the leeks in the skillet cut side down, and cook for 5 to 6 minutes. Season with salt and pepper, and pour the veggie broth into the skillet. Slice half of the orange into slices (reserve the rest for later), and snuggle those next to the leeks along with the thyme sprigs. If you are using a pretty big skillet, you may need a little more broth. Cover, and let the leeks braise for 10 to 12 minutes. They should be fork-tender and fully caramelized/charred on the cut sides.
While the leeks are cooking, combine the ingredients for the pomegranate relish in a small bowl. Serve the leeks warm with spoonfuls of the relish.
Caramelized leeks are best enjoyed right away with a fork and knife.
The pomegranate relish can be made up to a few days in advance and stored in an airtight container in the fridge.