Lay out the puff pastry sheets to thaw.
Preheat oven to 375 degrees F (220 degrees C).
Heat the oil in a nonstick pan over medium heat; saute the mushrooms and onions; saute until soft and all the liquid has evaporated. Mix in the thyme. Season with salt.
Overlap the puff pastry according to the amount of space you need to fit the filling. Evenly spread the mushroom mixture into the center area of the puff pastry.
In a bowl mix ground chicken, milk, breadcrumbs, worchestershire sauce, season with salt and pepper. Form the mixture into a loaf and set it on top of the mushroom mixture/puff pastry.
Fold in the ends of the puff pastry and wrap it around the chicken like a burrito. Place it seam side down on a parchment paper lined baking sheet.
Bake for about 25 - 35 minutes until the internal temperature reaches 160 degrees using a thermometer and the puff pastry is golden brown. Once done, remove from the oven and set aside for 3 - 5 minutes before slicing into portions.
For the gravy: In a saute pan over medium heat melt the butter and stir in the flour, cook for 1 minute. Stir in the broth and simmer until the sauce thickens and becomes smooth. Season with salt and pepper to taste.
Serve with gravy, garnish with thyme sprigs.