Make the filling: Preheat the oven to 375 degrees Fahrenheit. Set a large dutch oven or heavy bottom skillet over medium heat and add in butter. Once the butter has melted, add diced onion and cook until translucent, about 3-5 minutes. Add thyme, garlic, flour, salt, and cracked pepper and stir until pasty, about 1-2 minutes.
Pour in liquids: Add chicken broth and wine. Bring mixture to a simmer, about 5-10 minutes. The sauce will have thickened. Add half and half and stir.
Add veggies and chicken: Stir in potatoes, frozen peas, carrots and chicken. Cook for 5-10 minutes, stirring frequently.
Bake: Transfer to a large greased casserole dish and bake for 25-30 minutes, or until the mixture is bubbling and the potatoes are fork tender.
Top with puff pastry: Remove casserole from oven and top with 1 sheet of thawed puff pastry (if desired, cut pastry with a circle cookie/biscuit cutter).Continue to bake the casserole according to pastry package directions (mine took about 20 minutes) until the pastry is flaky and golden. Garnish and serve: Let casserole cool for 5-10 minutes, then top with chopped parsley. Enjoy!