Peel and dice the potatoes into roughly 2 cm cubes, creating even pieces for uniform cooking.
Heat the olive oil in a large pot over medium heat until shimmering, and add the chopped onion. Cook, stirring occasionally, until the onion becomes translucent and fragrant, about 5 minutes, filling your kitchen with a sweet aroma.
Add the minced garlic to the onions and cook for another minute, stirring constantly, until the garlic is fragrant and slightly softened.
Stir in the diced potatoes, ensuring they are coated with the fragrant onion and garlic mixture. Pour in the vegetable broth, making sure the potatoes are mostly submerged. Bring the mixture to a boil, then reduce the heat to low and cover the pot.
Let the soup simmer gently for 20 to 25 minutes, or until the potatoes are extremely tender and easily pierced with a fork, filling your kitchen with a cozy, earthy scent.
Carefully insert the immersion blender into the pot and blend the soup directly until smooth and velvety, about 1-2 minutes. Alternatively, transfer the soup in batches to a blender, blend until smooth, then return to the pot.
Stir in the plant-based milk to add creaminess, then season to taste with salt and pepper. If desired, add a squeeze of lemon juice to brighten the flavors and balance the richness.
Give the soup a good stir, taste again, and adjust the seasoning as needed. It should be warm, thick, and smooth, with a comforting aroma inviting you to serve.
Ladle the hot soup into bowls, garnish with fresh herbs if desired, and drizzle with a little olive oil or a sprinkle of pepper for an extra touch. Serve immediately while steaming and fragrant.