Peel and chop the potatoes into 2 cm cubes, setting them aside in a bowl.
Heat the olive oil in a large pot over medium heat until it shimmers and begins to smell fragrant.
Add the diced onion to the pot and sauté for about 5-7 minutes, stirring occasionally, until it turns golden and releases a sweet aroma.
Stir the chopped potatoes into the onion mixture, coating them with oil, and cook for another 2 minutes to start softening the potatoes.
Pour in the vegetable broth, bringing the mixture to a gentle boil. Once bubbling, reduce heat to low, cover, and let simmer for 15-20 minutes, until the potatoes are fork-tender and the kitchen smells earthy and warm.
Use an immersion blender to carefully blend the soup directly in the pot until smooth and velvety, or transfer in batches to a blender and puree until creamy.
Stir in the plant-based milk and heat for another 3-5 minutes, until warmed through and slightly thickened. Taste and season with salt and pepper as desired.
Once the seasoning is adjusted to your liking, ladle the hot, creamy soup into bowls and serve immediately, perhaps garnished with fresh herbs or a drizzle of olive oil for extra flair.