Start by peeling and chopping the potatoes into 2-cm cubes, making sure they’re evenly sized for uniform cooking.
Heat the olive oil in a large heavy-bottomed pot over medium heat until it shimmers and begins to smell lightly fragrant.
Add the diced onion to the pot and sauté, stirring occasionally, until it becomes translucent and starts to soften, about 5 minutes. The onion should smell sweet and look glossy.
Stir in the minced garlic and cook for another minute until fragrant, taking care not to brown it.
Sprinkle the smoked paprika, cumin, and a pinch of chili flakes over the aromatics, stirring constantly for about 1 minute until the spices release their aroma and turn a deeper color.
Add the chopped potatoes to the pot, stirring to coat them evenly with the spice mixture.
Pour in the vegetable broth, ensuring the potatoes are fully submerged, then bring the mixture to a boil.
Reduce the heat to low and let the soup simmer gently for about 20 minutes, or until the potatoes are very tender and breaking apart easily when pierced with a fork.
Use an immersion blender directly in the pot to blend the soup until it’s smooth and velvety, or transfer carefully to a blender in batches and blend until silky.
Stir in the coconut milk, mixing well to incorporate the creamy richness, and heat through for another 2-3 minutes.
Taste the soup and season with salt and pepper as needed, adjusting the spice levels to your preference.
Serve hot, garnished with chopped herbs like parsley or chives if desired, and enjoy the cozy, smoky flavors in every spoonful.