Melt butter in a large pot. Add onions, celery and carrots. Season with salt, paprika and pepper and cook until onions are translucent, about 5 minutes. Pour in chicken stock and bring to a slow boil.
Add noodles and cook until tender, about 10 minutes. After noodles are fully cooked, add the broccoli. Dissolve cornstarch in milk and slowly stir into slowly boiling soup. Cook until slightly thickened, about 5 minutes.
Remove from heat and stir in cheese until fully melted. Add parsley and additional salt and pepper to taste, if needed. Enjoy!