Peel and chop the potatoes into roughly 1-inch cubes, then set aside.
Dice the onion into small, even pieces; this helps it cook quickly and evenly.
Heat the large pot over medium heat, then add a tablespoon of olive oil. Once shimmering, add the diced onions and cook, stirring occasionally, until they turn translucent and smell sweet, about 5 minutes.
Add the chopped potatoes to the pot, stirring to coat them in the flavorful onion oil. Pour in the vegetable broth, then add a pinch of salt. Bring everything to a gentle boil.
Reduce the heat to low and let the mixture simmer until the potatoes are very tender and easily pierced with a fork, about 15-20 minutes. You should see the potatoes soften and the broth slightly thickening.
Use an immersion blender to carefully blend the soup directly in the pot until smooth and velvety. If you don’t have an immersion blender, transfer the soup in batches to a blender, blend until smooth, then return to the pot.
Stir in the plant-based milk, mixing well to incorporate. Squeeze in the juice of half a lemon, then taste and adjust the seasoning with salt and pepper as needed.
Let the soup rest for a few minutes to allow flavors to meld. The final texture should be creamy and smooth, with a bright, fresh aroma from the lemon.
Serve the hot soup in bowls, garnished with fresh herbs or a drizzle of olive oil if desired. Enjoy the comforting, velvety warmth in every spoonful!