Melt 2 tablespoons butter in a large stock pot. Add the chicken, sprinkle with salt and pepper and cook for 6-7 minutes or until cooked through. Remove from pot and set aside.
Add remaining 2 tablespoons butter along with carrots, celery, onions, and potatoes. Cook for about 8 minutes or until tender. Add the garlic and cook another 30 seconds.
Mix in the flour, salt, and pepper and cook for 1 minutes stirring constantly. Stir in the milk, cream, bouillon, and thyme. Bring to a boil, reduce heat and simmer for about 2 minutes or until thickened.
Add the chicken and peas and cook for 3 more minutes. Serve soup with puff pastry.
For the Puff Pastry:
Preheat oven to 400 degrees F and line a baking pan with parchment paper.
Cut puff pastry out with a cookie or biscuit cutter and place on lined baking sheet. Brush with egg mixed with 1 tablespoon water and then bake for 12 minutes until golden. Serve with soup.