Preheat the oven to 400 degrees. Cut pastry sheet into 1-inch-wide strips. On a baking sheet, weave strips into a lattice pattern to fit the size of your baking dish.
Heat 2 1/2 cups broth, sweet potatoes, russet potatoes, onion, celery, and garlic in a large skillet over medium-high heat. Cook until the vegetables are slightly soft, about 8 minutes.
Whisk together the remaining 3/4 cup broth, cream, and flour. Pour the slurry into the vegetable mixture; cook and stir until thick and bubbly.
Add chicken, apple, and peas. Season with salt and pepper. Pour into prepared baking dish and dot with 2 tablespoons unsalted butter.
Fit the pastry over the baking dish and crimp edges. Place a baking sheet under the baking dish or on the rack below the baking dish to catch drips.
Bake for 25 to 30 minutes, or until the pastry is nicely browned.