In a large stock pot, melt butter. Add diced onion and chopped celery, and saute over medium heat until soft and translucent.
Increase heat to medium-high, and add chopped chicken into the pot and cook until lightly browned. Don't worry if it isn't cooked all the way through, it will finish cooking in the broth.
Add chicken broth and fresh carrots. Simmer over medium-low heat for 20 minutes. Add frozen peas and green beans. Combine the corn starch and cold water, and whisk until combined. Pour into the simmering soup while stirring. Return to a simmer for 5 minutes. Add poultry seasoning and cream. Add salt to taste.
Serve with sliced, baked pie crust slices, rolls, and salad for a complete meal!