Melt butter in a pot, sauté garlic paste and sliced carrot for 2 minutes.
Add chicken breast and vegetable broth; simmer covered for 20 minutes.
Remove cooked chicken, shred into bite-sized pieces, and return to broth.
Add noodles, black pepper, and salt; simmer for 5 minutes until noodles are tender.
Serve hot in deep bowls.