Slice all veggies using a mandoline. You can also slice them with a sharp knife, but a mandoline will make even and thin slices.
Place the chopped tomatoes, balsamic vinegar, garlic and Italian spices in the slow cooker.
Season generously with salt and pepper, and mix to combine. Add half of the grated parmesan.
Layer the sliced veggies on top. Make a spiral-shaped stack of veggies, then drizzle olive oil. (NOTES - The best way to make the spiral, is to pick each veggie slice and build a small stack in your hand. Then place it into the slow cooker following its edges all the way around.)
Add in the remaining parmesan. Season to your taste and sprinkle fresh thyme.
Cover and cook on HIGH for 2-3 hours or on LOW for about 4-5 hours. NOTE: If you cook on HIGH check it after 2 hours. If you cook on LOW check it after 4. Cooking time depends on how thick the veggie slices are, and on the model of your slow cooker.
You can also make this recipe in the oven. Replace the slow cooker with a round oven-proof dish or a cast iron pan and cook it in the oven for about 1.5 hours, at 350F/180C.The ingredients remain the same.