Spray a Dutch oven with cooking spray. Heat pan over medium heat. Add onion and garlic to pan; cook 4 minutes, stirring occasionally to prevent burning.
Add cauliflower rice and 1 cup water. Cover pan, increase heat to medium-high, and cook until tender, 5 to 6 minutes.
Scrape mixture into a blender. Add remaining 2 cups water, thyme, salt, and pepper. Blend on high speed until very smooth, about 1 minute. Pour soup into pan and cook over medium heat until thoroughly heated, about 1 minute (or puree soup in pot using an immersion blender). Garnish with additional thyme and pepper.