Soup: Heat 1 Tbsp oil in a large pot over medium heat. Add onion and garlic, cooking until onion softens (about 5 min). Add broth, nutritional yeast, and thyme. Roughly chop about 3/4 of the cauliflower and add to the pot. Cover and simmer for 15 to 20 minutes, until cauliflower is fork-tender.
Crispy Bits: Thinly slice the remaining 1/4 of the cauliflower. Heat remaining oil in a large skillet over medium heat, then add cauliflower in a single layer. Cook until both sides are lightly browned, then add the panko and continue cooking until bread crumbs are golden. Season with salt and pepper.
Serve: Remove thyme sprigs from soup and puree (either using a handheld immersion blender or a by transferring to a standing blender). Season with salt and pepper to taste. Serve warm topped with crispy cauliflower.
For a low carb option, simply leave out the panko!