Sauté Vegetables: In a large pot, heat the olive oil over medium heat. Add the chopped onion, garlic, carrots, and celery. Sauté for about 5-7 minutes, until the vegetables begin to soften.
Cook Potatoes: Add the diced potatoes and vegetable broth to the pot. Bring the mixture to a boil, then reduce the heat and simmer for 15-20 minutes, or until the potatoes are tender.
Blend the Soup: Once the vegetables are soft, use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, transfer the soup to a blender in batches, then return it to the pot.
Add Cream: Stir in the heavy cream or coconut milk, and season with thyme, rosemary, salt, and pepper. Let the soup simmer for another 5 minutes to heat through.
Serve: Once heated, serve the soup hot, topped with freshly chopped herbs or a sprinkle of cheese if desired.