Preheat the oven to 400 degrees F. Heat 2 tablespoons olive oil in a Dutch oven or heavy-bottomed pot over medium-high heat. Add the onion, carrot, celery seeds and garlic and cook, stirring occasionally, until the onion softens, about 3 minutes. Add 1/3 cup flour, the Worcestershire sauce and hot sauce; cook, stirring occasionally, about 2 minutes. Add the chicken broth and 2 cups water and bring to a boil. Reduce the heat to medium low and cook until the vegetables are tender, about 20 minutes.
Meanwhile, toss the bread cubes with 1 tablespoon olive oil on a baking sheet; season with salt and pepper. Bake until golden and crisp, about 7 minutes; set aside.
Puree the soup in a blender until smooth. Return to the pot and bring to a boil, then reduce the heat to medium low and simmer 5 minutes. Toss the cheddar, provolone and the remaining 2 tablespoons flour in a bowl; slowly whisk the cheese mixture into the soup until melted. Return to the blender and puree until smooth. Pour back into the pot and bring to a low boil; remove from the heat.
Heat the remaining 2 tablespoons olive oil in a large skillet over medium-high heat. Add the beef and cook, stirring occasionally, until browned, about 3 minutes. Stir in the pepperoncini and parsley and season with salt and pepper. Ladle the soup into bowls; top with the beef, croutons and more parsley.