Over medium heat, heat olive oil in a large, heavy bottom stockpot or Dutch oven. Once hot, add onion and leeks and cook for 4-5 minutes, stirring frequently, or until onions are soft and fragrant. Add minced garlic, Italian seasoning and mushrooms to the pot and stir to combine. Cook for 3-4 minutes before adding the chopped carrots. Stir and cook for 1-2 minutes.
Increase heat to high and carefully add 8-10 cups of water or vegetable broth to the pot. Stir in the chopped cauliflower, zucchini, and bay leaves to the pot and bring to a boil.
Reduce heat to low, cover and cook soup for at least 45 minutes to 2 hours, or until all vegetables are soft and fully cooked. Carefully stir in the oats and chopped kale and continue to cook for 10-15 minutes. Season with a few generous pinches of salt (especially if you used water as the base) and fresh cracked pepper.