In a large pot, melt the butter over medium heat.
Add the chopped onions and garlic; sauté until translucent.
Stir in the diced carrots and potatoes; cook for 5 minutes.
Sprinkle flour over the vegetables; mix well to coat.
Gradually add chicken broth, stirring continuously to prevent lumps.
Bring the mixture to a boil, then reduce heat to simmer.
Add shredded chicken, peas, and thyme; simmer for 15 minutes.
Stir in heavy cream; season with salt and pepper.
Simmer for an additional 5 minutes until heated through.
Serve hot, garnished with fresh herbs if desired.