In a large soup pot, heat the one tablespoon of the olive oil over medium high heat. Add the onion and cook till nearly translucent, now add the garlic. Don't let the garlic brown and saute another couple of minutes.
Add the rest of the chopped veggies, sauteing for just a minute or two. You're not cooking them just sauteing for the wonderful flavor this quick step will infuse in your soup. Add the thyme and salt and pepper while sauteing.
Now put the veggies in the crock-pot, add the tomatoes and broth. Cook on low 7-9 hours (depending on your crock-pot) or high 4-6 hours (but all crock-pots are different, depending on size, age, brand etc. Remember, your mileage may vary). Just before serving, gently mash some of the potato chunks against the side of the crock-pot to thicken the soup, give it a stir and serve.