Heat olive oil in a large pot over medium-low heat. Add carrots, onions, and celery. Saute for 5-7 minutes.
Add 3 tablespoon of vegan butter, thyme, and garlic. Cook for 1 minute, then sprinkle everything with flour and cook for another minute.
Add cauliflower, peas, and corn. Cook for 3 minutes.
Pour in 1 cup of stock and add vegan cream cheese. Stir well, then add another 3 cups of stock and 1 can of tomatoes. Lower the heat to a minimum and let the soup simmer for 30 minutes.
Finally, add beans and let them heat through for another 2-3 minutes. Adjust the seasoning to your liking before serving the soup.
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Notes
For added flavor, include 1 tablespoon of Italian herbs, ½ teaspoon curry powder, or ½ teaspoon each of onion powder and garlic powder.
Roast the vegetables in the oven before adding them to the stockpot for the soup for extra flavor.
Make your own homemade vegetable broth by boiling down vegetable peels and end pieces for 1 hour, strain, and save the remaining liquid.
Substitute the vegan cream cheese with vegan sour cream or skip for a broth-based soup.