Start by peeling your potatoes and chopping them into small cubes. Once you're finished, go ahead and chop the rest of your vegetables (the carrots, celery, onions, and garlic).
Next, heat a large pot on the stove over medium heat, and add in your oil.
Once the oil is hot, then add the onion, celery, and carrots. Stir until veggies begin to soften, about 5-6 minutes. Then, add the mashed garlic and stir for another minute.
Next, add in the diced potatoes, veggie broth, milk, thyme, salt, and pepper, making sure to stir everything well.
Lower the heat to low, cover, and simmer for about 30-32 minutes, until the potatoes are tender when touched with a fork.
Once the potatoes are done, transfer about 1/2-3/4 of the soup to a blender, and blend until creamy. Then, transfer it back to the large pot and stir together. You might have to work in batches, but that's okay! The key is that we still want some chunks in the soup while still keeping it creamy.
If the soup is too thick, you can add a touch of water until it's thinned out to your likeness.
Finally, plate, top with your desired garnishes, and serve. Enjoy!