Peel and chop the potatoes into small, even cubes to help them cook quickly and evenly. Set aside.
Heat the large pot over medium heat and add a tablespoon of oil. Once shimmering and fragrant, add the chopped onion. Cook for about 5-7 minutes, stirring often, until the onion turns golden and smells sweet.
Add the minced garlic and cook for another 30 seconds until fragrant, being careful not to burn it. The garlic should smell rich and slightly toasted.
Stir in the chopped potatoes, then pour in the vegetable broth. Bring the mixture to a gentle boil, then reduce the heat to low, cover partially, and let simmer for 15-20 minutes, or until the potatoes are very tender and breaking apart easily.
Once the potatoes are soft, remove the pot from heat. Use an immersion blender to carefully blend the soup directly in the pot until smooth and velvety. Alternatively, transfer in batches to a stand blender, blending until silky smooth.
Stir in the coconut milk and smoked paprika, then taste the soup and adjust with salt or more spices if desired. Add a splash of lemon juice to brighten the flavors.
Return the soup to low heat for 2 minutes, allowing the flavors to meld. Taste again and add more lemon or spices if needed.
Serve the hot soup in bowls, garnished with fresh herbs or a drizzle of oil if desired. Let it sit for 5 minutes to allow the flavors to settle and intensify.