Wash and peel the vegetables. Dice the onion and potato, slice the carrots and celery, and chop the green beans. Mince the garlic finely.
In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until translucent. Stir in the minced garlic and cook for an additional minute.
Add the sliced carrots, celery, and diced potato to the pot. Cook for about 5-7 minutes, stirring occasionally. Then mix in the chopped green beans and corn. Sprinkle in the dried thyme and basil, then pour in the vegetable broth. Bring to a boil, then reduce heat to low and let simmer for about 15-20 minutes until all vegetables are tender.
Blend the soup using an immersion blender or transfer in batches to a countertop blender until desired consistency is reached.
Return the soup to the pot if using a countertop blender. Stir in the heavy cream and season with salt and pepper to taste. Heat through for another 5 minutes.