Melt the butter in a large pot over medium heat. Add the leeks, onions, garlic, celery and carrots. Add the red pepper flakes and season with salt. Cook the vegetables, stirring occasionally, until they are beginning to soften and release their flavors, 6 to 8 minutes.
Stir in the tomato paste and thyme leaves and cook for 2 more minutes.
Add the corn, potatoes, tomatoes and vegetable stock. Season as needed with salt and pepper. Bring to a simmer and cook, stirring occasionally, until the potatoes are tender, about 40 minutes.
Divide the soup among bowls and garnish with the fresh parsley leaves, the reserved celery leaves and few cracks of black pepper