Heat olive oil in a large skillet or sauté pan over medium high heat. Add onions and celery and sauté until onions are translucent, about 3 to 4 minutes (stirring frequently). Add garlic and cook for an additional 30 seconds, stirring constantly.*
Transfer onion and celery mixture to your slow cooker insert with at least a 6 quart capacity.
Add potatoes, vegetable broth, diced tomatoes with juices, salt, pepper, Italian seasoning and bay leaves. Cover and cook on high heat for 6 to 7 hours, or until potatoes are tender. During the last 30 minutes of cook time, add drained canned vegetables and stir to combine. Cover and cook until vegetables are heated through.
Remove and discard bay leaves. Season with additional salt and pepper, if desired.
Ladle into bowls and sprinkle with chopped fresh parsley, if desired.