Slice potato, sweet potato, bell peppers, and red onion into thin rounds, about 1/4 inch thick. Slice zucchini and summer squash into slightly thicker rounds, about 1/2 inch. Toss vegetables with minced garlic and fresh thyme in a large mixing bowl.
Spread 1 cup of tomato pasta sauce over the bottom of the slow cooker.
Arrange the vegetables in layers standing up in the slow cooker, alternating between types. Season each layer with salt and pepper to taste and repeat until all of the vegetables have been used up.
Pour the remaining tomato sauce evenly over the vegetables. Replace the slow cooker lid and cook for 3-4 hours on high or 8-10 hours on low.
Sprinkle fresh basil and grated parmigiano reggiano cheese evenly over the top and serve.