Peel and dice the onion, garlic, carrots and potatoes. (Dice the potatoes into 1/2 ich cubes. The smaller that you dice the potatoes the faster they will cook.)
Add the diced onion to 3 tablespoons of olive oil and cook for 5 minutes over low heat. Add the minced garlic, salt, and smoked paprika then sauté for an additional 1 minute.
Add the vegetable broth, carrots, potatoes, and corn then turn up the heat to medium-high and bring the soup to a slow boil.
Cover and simmer for about 15 minutes until the potatoes are tender. (The size of the potato cubes will determine how long it will need to simmer.)
Add the plant-based milk and simmer for 5 more minutes. Then add additional salt and ground black pepper to taste or some Tony Chachere's for a little spice.
How to thicken the brothIf you prefer the broth make a vegan roux and add the broth to the roux to thicken it. You can also make a slurry out of 1/4 cup of potato starch or corn starch dissolved in 1/2 cup of cold water and add it to the soup.