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Gather all ingredients.
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Melt butter in a large (6-quart) stockpot over medium heat. Add onion. Cook and stir until softened, about 5 minutes. Add garlic and cook for 1 minute.
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Sprinkle flour over onion mixture; cook and stir for 1 minute. Gradually whisk in chicken broth until smooth. Stir in half-and-half, Italian seasoning, salt, and pepper. Bring to a boil.
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Add egg noodles and cook until al dente, stirring occasionally so the noodles do not stick together, about 5 minutes. (If using fettuccine, cook about 8 minutes.)
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Stir in broccoli florets and cook until crisp-tender, 3 to 5 minutes.
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Add chicken and Parmesan cheese; cook until heated through, 2 to 3 minutes.
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Ladle soup into bowls. Garnish with parsley and serve with additional Parmesan cheese.