Melt butter in a large saucepan or soup pot. Add onion, garlic, carrots, Italian seasoning, salt, and pepper, then cook over medium heat for about 10 minutes.
Whisk in flour. Slowly add broth and continue to whisk until everything is well combined. Add half and half.
Add noodles and bring to a boil.
Continue to cook over medium-high heat, stirring occasionally, 12-15 minutes, or until noodles and carrots are tender. Taste and add more salt if needed. Serve immediately.