Peel and chop the sweet potatoes into 1-inch cubes, then dice the onion and mince the garlic cloves.
Add the chopped sweet potatoes, diced onion, minced garlic, cinnamon, nutmeg, and vegetable broth into the slow cooker. Stir gently to combine everything evenly.
Set the slow cooker to low and cook for 6 to 8 hours, until the sweet potatoes are very soft and fragrant, filling the air with a warm aroma.
Once the cooking time is up, insert an immersion blender directly into the slow cooker and blend the mixture until completely smooth and velvety. Alternatively, transfer the hot soup in batches to a blender, blending until smooth, then return to the pot.
Stir in the coconut milk and season with salt and pepper to taste. Warm the soup gently for another 5 minutes, allowing the flavors to meld and the soup to heat through.
Check the seasoning and adjust with more salt or pepper if needed. Serve hot, garnished with fresh herbs or a drizzle of coconut milk if desired.