Heat a deep pot over medium-high heat with the EVOO. Add the onion, garlic, potatoes and zucchini. Cook until softened, about 7-8 minutes.
Add the tomatoes and chicken stock to the pot, and season with salt and freshly ground black pepper. Bring the soup up to a boil then turn it down to a simmer. Cook for 8-10 minutes. Taste and re-season.
While the soup is simmering, heat a large, nonstick skillet over medium-high heat. Add 1/4 cup of cheese in a small mound to the skillet. Repeat with the remaining cheese, making sure to keep each mound at least a half inch apart from the others. Cook for 3-5 minutes or until golden and crisp. Transfer to a cooling rack.
To serve, ladle the soup into a bowl and top with a cheese crisp. Garnish with basil.