Peel the potatoes and chop them into 2-cm cubes, setting them aside.
Heat olive oil in a large pot over medium heat and add the chopped onion. Sauté until it becomes translucent and fragrant, about 5 minutes, with a gentle sizzle filling the kitchen.
Add the minced garlic to the pot and cook for another minute until it turns golden and releases a warm, spicy aroma.
Toss in the chopped potatoes, stirring to coat them in the aromatic oil and vegetables, and cook for 2 minutes until slightly softened and fragrant.
Pour in the vegetable broth, bringing the mixture to a gentle boil. Once bubbling, reduce the heat to low, cover the pot, and let it simmer for 15-20 minutes until the potatoes are fork-tender and easily mashable.
Use an immersion blender directly in the pot to blend the soup until smooth and velvety, or blend in batches in a blender if you prefer a creamier texture. Be cautious of hot splashes!
Stir in the coconut milk or plant-based cream, mixing until fully incorporated and the soup appears glossy and rich.
Season generously with salt and pepper, tasting as you go, until the flavors are balanced and inviting.
Allow the soup to simmer uncovered for another 5 minutes to meld all the flavors together, with a gentle bubbling sound.
Serve the hot soup in bowls, garnished with chopped chives or green onions for a fresh, vibrant touch.