Finely mince ¼ cup (60 mL) of red pepper, and reserve, along with ¼ cup (60 mL) corn for garnish. Heat the vegetable oil over medium heat in a pot large enough to hold all the ingredients. Add the onion, celery, leek, and garlic; cover to sweat, stirring occasionally, until the vegetables have begun to soften but not brown, about 6 to 7 minutes.
Add the remaining red peppers and enough water to just cover the vegetables, about 4 cups (950 mL). Cover and simmer for 30 to 40 minutes or until the peppers are soft. Add the remaining corn, water or stock, and the thyme, rosemary, and cayenne; simmer for another 5 minutes. Using a hand blender, or in a blender or food processor, roughly purée the soup in batches and season with salt and pepper.
When ready to serve, top each bowl with a sprinkling of corn and red pepper.