Bring a large pot of water to a boil. Once boiling, add the chicken drumsticks and boil for 25 minutes until cooked through. Drain the water. Remove the skin and shred the chicken off of the bone.
Preheat the oven to 400 F
Add the olive to a large braiser pan or skillet, one that's at least 10-12″ wide and holds about 3 quarts. Add in the diced onion and saute for about 5-6 minutes.
Add the bag of frozen mixed vegetables, diced sweet potato, spices, fresh thyme and flour. Toss together.
Pour in the broth, milk and the shredded chicken and mix well.
Cover the pan and bring it to a boil. Once boiling, reduce the heat to low and simmer for 10 minutes until the sauce thickens. Remove the pan from the heat. Adjust salt if needed.
Roll out the puff pastry to thin it out so its large enough to fit over the filling. Cover the filling with the rolled out pastry sheet, overlapping the edges into the pan.
Whisk an egg in a small bowl and brush the top of the puff pastry with the egg. Poke a few holes with a fork throughout the pastry sheet.
Bake for 25-30 minutes, until browned. Let stand for 10 minutes before cutting into it.