In a large pot, cook the onion, celery, and carrot over medium heat in 1 cup of the vegetable stock for 5 minutes. Add the garlic, bell pepper, and potatoes and cook for 2 more minutes. Add the remaining 4 cups of vegetable stock and the broccoli, thyme, salt, and black pepper, and bring to a boil over high heat. Cover and simmer until the broccoli and potatoes are soft, about 10 minutes.