In a large soup pot*, heat the olive oil over medium-high heat; add the onion and cook until nearly translucent. Add the garlic and sauté for a couple of minutes, but don’t let it brown!
Add remaining veggies; sauté for just a minute or 2 (you’re not cooking them, just getting the wonderful flavor this quick step will infuse in your soup). Add the thyme, salt and pepper while sautéing.
Now place the veggies in a large slow cooker; add diced tomatoes and broth. Cover and cook on LOW for 7 to 9 hours or on HIGH for 4 to 6 hours (all slow cookers differ, depending on size, age, brand, etc…your mileage may vary). If your slow cooker isn’t large enough, simmer the mixture in the soup pot on the stovetop for at least 1 hour.
Just before serving, gently mash some of the sweet potato chunks against the side of the slow cooker or soup pot to thicken the soup; give it a stir and serve.