Cook the vegetables: In a large pot, warm the olive oil over medium heat. Incorporate the chopped onion, sliced celery, and carrots. Sauté for about 5 to 7 minutes, stirring occasionally, until the vegetables become tender.

Season and add potatoes: Add the salt, black pepper, and dried thyme to the pot, then stir in the diced potatoes and minced garlic. Cook for another 2 minutes, allowing the garlic to become fragrant.

Simmer the soup: Pour in the vegetable broth, ensuring the vegetables are fully submerged. Bring the soup to a boil, then reduce the heat to low and let it simmer for 15-20 minutes, or until the potatoes are tender.

Add the frozen vegetables: Stir in the frozen peas and corn, allowing them to cook for another 5 minutes.

Make it creamy: Reduce the heat to low and slowly stir in the milk or plant-based milk. Allow the soup to gently warm for another 5 minutes without boiling, ensuring the milk blends into the broth.

Adjust seasoning: Taste the soup and adjust the seasoning if needed, adding more salt or pepper to your preference.

Dish it out: Spoon the soup into bowls and top with a sprinkle of freshly chopped parsley. Enjoy it warm alongside some crusty bread or a refreshing side salad.