Peel and chop the sweet potatoes into 2-inch chunks, aiming for uniform pieces so they cook evenly.
Dice the yellow onion and mince the garlic, preparing to add flavor to the soup.
In a skillet over medium heat, warm the olive oil until it shimmers and becomes fragrant.
Add the diced onion and sauté until translucent and fragrant, about 5 minutes. The onions should soften and turn a light golden color.
Add the minced garlic and cook for another minute until fragrant, filling your kitchen with a warm, savory aroma.
Transfer the sautéed onion and garlic to your slow cooker.
Add the chopped sweet potatoes to the slow cooker, then pour in the vegetable broth.
Sprinkle the smoked paprika, cumin, and a pinch of salt and pepper over the ingredients in the slow cooker.
Set the slow cooker to low and cook for 6-8 hours, until the sweet potatoes are very tender and start to fall apart, filling your home with a smoky, sweet aroma.
Once cooked, carefully blend the soup directly in the slow cooker using an immersion blender until smooth and velvety. Alternatively, transfer in batches to a regular blender and blend until smooth, then return to the pot.
Stir in the coconut milk, mixing thoroughly to create a rich, creamy texture with a tropical hint. Taste and adjust seasoning with salt and pepper as needed.
Serve the soup hot, garnished with a swirl of coconut milk or fresh herbs if desired, and enjoy the velvety, smoky warmth in each spoonful.