Peel the potatoes and chop them into 2-cm cubes, creating even-sized pieces for uniform cooking.
Heat a large heavy-bottomed pot over medium heat, then add the olive oil. Once shimmering, toss in the diced onion and cook for about 3-5 minutes until fragrant and translucent, filling your kitchen with a gentle aroma.
Add the minced garlic to the pot and cook for another minute, stirring constantly to prevent burning, until the garlic releases its aromatic scent and turns slightly golden.
Stir in the chopped potatoes, coating them with the aromatics, and then pour in the vegetable broth. Turn up the heat and bring everything to a gentle boil, watching the liquid bubble softly.
Reduce the heat to low, cover the pot, and let the potatoes simmer for about 15-20 minutes until they are tender and easily pierced with a fork, filling the air with the comforting scent of cooked potatoes.
Turn off the heat and carefully use an immersion blender directly in the pot to blend the mixture until smooth and velvety. Alternatively, transfer the mixture in batches to a blender and blend until silky, then return it to the pot.
Stir in the coconut milk, mixing well to incorporate its creamy richness. Warm the soup over low heat for about 5 minutes, stirring occasionally, to meld the flavors without boiling the coconut milk.
Season the soup with salt and freshly ground pepper to taste, adjusting as needed for balance and depth. If desired, add chopped fresh herbs for a burst of flavor and color.
Ladle the hot, velvety soup into bowls, garnishing each with herbs or a drizzle of olive oil if you like, and serve immediately for the best comfort and flavor.
Enjoy this warm, nourishing bowl of vegan potato soup, perfect for cozy evenings and chilly days.