In a large stockpot or Dutch oven, heat olive oil over medium heat. Add vegetable mix and cook until vegetables begin to soften, add garlic and cook another minute. Remove vegetables and set aside.
Add ground beef to the same pot and cook until crumbled and cooked through. Season beef with basil, oregano, salt, and pepper. If desired, stir in yellow mustard and pickles.
Combine vegetables and the beef in the pot, stir in chicken broth. Bring broth to a boil. Add pasta and reduce heat. Partially cover the stockpot and allow the pasta to cook until al dente.
Whisk together the milk and the flour, pour milk into the soup, stir until the soup has slightly thickened. Add cheese and stir until melted. Stir in Greek yogurt just before serving.