Peel and chop the potatoes into uniform 2-cm cubes, then set aside.
Heat the olive oil in a large pot over medium heat, until it shimmers and starts to smell fragrant.
Add the chopped onion to the pot and cook, stirring occasionally, until it becomes translucent and soft, about 5 minutes. You’ll notice a gentle sizzle and the aroma will deepen.
Stir in the minced garlic and cook for an additional 30 seconds, just until fragrant. Be careful not to burn it—you're aiming for a golden aroma.
Add the chopped potatoes to the pot, stirring to coat them with the aromatic mixture. Cook for 2-3 minutes, allowing the potatoes to start absorbing the flavors.
Pour in the vegetable broth, bringing the mixture to a boil. Once bubbling, reduce the heat to low, cover the pot, and let it simmer for 20-25 minutes until the potatoes are fork-tender and soft.
Remove the pot from heat and use an immersion blender to carefully purée the soup directly in the pot until smooth and velvety. Alternatively, transfer the soup in batches to a blender, then return it to the pot.
Stir in the plant-based milk and season with salt and freshly ground pepper. Warm the soup gently over low heat for 5 minutes, stirring occasionally, but do not let it boil.
Check the seasoning, adjusting salt and pepper as needed. The soup should be smooth, creamy, and steaming hot, ready to serve.
Ladle the hot soup into bowls and garnish with fresh herbs or a drizzle of olive oil for an inviting presentation. Enjoy the comforting warmth of this velvety vegan potato soup!