To a soup pot over medium-high heat, add EVOO. To the hot oil, add veggies and corn, and season liberally with salt and pepper. Sauté until tender, 8-10 minutes.
Add the tomatoes to the pot and cover with a tight-fitting lid. Cook 8-10 minutes more, until tomatoes burst. Add chicken stock, replace cover and bring up to a bubble.
Fill a food processor with the herbs and pulse to chop. Add a splash of stock and stream in EVOO with the machine running to form a green sauce. Season with salt and pepper.
Season soup with salt and pepper to taste. Serve in bowls topped with a heaping spoonful of herb sauce to stir in.