Preheat your oven to 450° F.
Slice an entire head of garlic in half (around the top). Wrap it in foil and place on a baking sheet. Chop up all your remaining vegetables into large chunks. Place them on the baking sheet. Drizzle with extra virgin olive oil. If you want to keep this recipe oil-free, drizzle with vegetable stock. Then, sprinkle with sea salt, black pepper, and sprigs of fresh thyme. Place baking sheet in the preheated oven and bake for about 45 to 55 minutes (when the carrot and sweet potatoes are fork tender). Allow everything to cool to room temperature.
Add the roasted carrots, the roasted garlic cloves (squeeze them out), and other roasted vegetables to a high-powered blender or regular stand blender, together with gochujang, lemon juice (or pickling juice), silken tofu, and half the vegetable stock. Blend on high until totally smooth, about 3 minutes.
Transfer the contents of the blender to a large Dutch oven or large pot. Over low heat, whisk in the remaining vegetable broth until totally incorporated and you obtain a beautiful, smooth, velvety broth. Remove from heat. Optional garnish includes kimchi, a little bit of chili oil, and celery leaves.