Heat a large pot on medium-high heat. Once hot, add the extra-virgin olive oil, chopped onion, and garlic. Sauté until soft for around 5 minutes.
Add fresh peas and potatoes and stir for 30 seconds to a minute to give it time to absorb all the flavors. Then add the vegetable broth and almond milk. Bring to a boil, then reduce the heat and let it simmer for about 10 minutes until the potatoes are tender (check with a fork).
Remove from the heat, stir in the mint, parsley, and basil and let the fresh herbs wilt for a minute.
Use an immersion blender, or pour the soup into a standard blender, and blend until smooth. Depending on how thick you like your soup, you can add an extra cup of broth, a bit at a time, and keep blending.
Taste and adjust for seasoning. If needed, reheat the soup in the pot until it's hot and steamy. Remove from the heat, add the lemon juice and stir well. Serve in individual bowls, and top it with some extra herbs.