In a large saucepan, combine turkey, carrots, celery, onion, bay leaves, and thyme. Pour over chicken broth and set pan over high heat. Bring to a boil. Reduce heat to medium and simmer 5 minutes, until liquid reduces slightly. Remove bay leaves. Remove from heat and stir in peas.
Transfer turkey mixture to a deep-dish pie plate or shallow casserole dish placed on a baking sheet. Spoon mashed potatoes over top and, using the back of a spoon, make an even layer.
Place pie on a baking sheet and bake 15 minutes, until top is golden brown and filling is bubbly.
Serving suggestion: Serve the pie with a bagged green salad.