In a dutch oven or heavy bottomed pot, heat coconut oil over medium heat.
Saute chopped shallots until soft and translucent, about 3 minutes. Add chopped roasted red peppers and seasonings. Stir well to combine, allow to cook 2-3 minutes.
Add cauliflower, stock, vinegar and fresh thyme. Bring to a simmer, cover pot and allow to cook for 10-15 minutes or until the cauliflower is very soft and falling apart.
Carefully working in small batches, puree soup until smooth in your blender*. Return fully blended soup back onto the stove and gently mix in the coconut milk.
Notes
*You may also use an immersion blender to puree your soup. Feel free to leave some chunks if you prefer, but I think it's best completely smooth.