Peel the potatoes and cut them into roughly 2-cm cubes, creating uniform pieces for even cooking.
Dice the onion into small, even pieces and crush or finely mince the garlic cloves.
Heat a large pot over medium heat and add a tablespoon of olive oil. Once shimmering, add the diced onions and cook, stirring occasionally, until they become translucent and fragrant, about 5 minutes. You should notice a gentle sizzle and the onions turning a soft, golden color.
Add the crushed garlic to the pot and cook for about 1 minute, stirring frequently, until it releases a fragrant aroma without browning too quickly.
Stir in the chopped potatoes, coating them with the onion and garlic mixture. Cook for 2-3 minutes, allowing the potatoes to absorb the flavors and start to soften slightly.
Pour in the vegetable broth, making sure the potatoes are fully submerged. Turn up the heat to bring the mixture to a gentle boil, with bubbling sounds and steam rising from the surface.
Reduce the heat to low and let the soup simmer uncovered for about 20 minutes, or until the potatoes are tender and easily pierced with a fork. The broth should slightly thicken and the aroma of cooked potatoes and garlic will fill your kitchen.
Use an immersion blender directly in the pot to blend the soup until smooth and velvety, or transfer in batches to a blender. Be careful with the hot liquid and blend until the texture is silky, with no lumps remaining.
Stir in the plant-based milk to add creaminess, and season with salt and pepper to taste. Let the soup simmer gently for another 5 minutes, adjusting the seasoning as needed. The soup should be warm, thick, and inviting, with a smooth, glossy surface.
Serve the hot soup in bowls, garnished with fresh herbs like chives or a drizzle of olive oil if desired. Enjoy this cozy, silky vegan potato soup with a slice of crusty bread or simply on its own for a satisfying meal.