In a large pot, melt butter over medium heat.
Add onion, carrots, and celery; sauté until softened, about 5 minutes.
Stir in garlic and cook for 1 minute until fragrant.
Sprinkle flour over the vegetables and whisk constantly for 2 minutes to create a roux.
Slowly pour in chicken broth while whisking to avoid lumps.
Add diced potatoes and thyme; bring to a boil, then reduce heat and simmer for 10-15 minutes until potatoes are tender.
Stir in cooked chicken and frozen peas; cook for 5 more minutes.
Pour in heavy cream and season with salt and pepper to taste.
Heat through without boiling, then remove from heat and serve warm.