Heat a medium soup pot over medium heat. Add extra-virgin olive oil, bay, chopped garlic and onions and let them sweat out while you prepare the rest of the veggies. Work next to the stove and drop as you chop, in order of longest cooking time: potatoes, eggplant, zucchini, and bell pepper. Season with salt and pepper, cover and cook 10 minutes, stirring occasionally. Uncover and add tomatoes and stock and cook 5 minutes more, to heat through. Turn heat off and stir in basil.
Char bread under broiler and rub with cracked garlic then drizzle with extra-virgin olive oil, top with cheese and pepper and return to the broiler for 30 seconds to brown cheese. Serve cheese whole-grain toast with bowls of vegetable stew.