Preheat oven to 450°F. In a large saucepan, cook vegetables in 2 tablespoons stock until softened, about 5 minutes. Stir in chicken. Remove from heat and set aside.
For the sauce:
In a medium saucepan, melt butter over medium heat. Stir in flour, onion, salt and pepper. Cook stirring constantly until mixture is bubbly. Stir in broth and milk. Heat to boiling, stirring constantly for 1 minute. Season to taste with Tabasco. Add sauce to chicken and vegetable mixture and stir well.
Transfer filling to pie dish. Top with pie pastry, seal edges well, and prick center to let steam escape. Bake for 10-12 minutes or until nicely browned.