Sauté: Heat the oven to 400°F (200°C). Cook the onion, carrots, and celery in butter for 7 to 8 minutes, then add the garlic.
Make the gravy: Stir in the flour for 1 minute, then the broth, Worcestershire, thyme, and sage. Simmer until thick, 3 to 4 minutes. Stir in the turkey and peas and season.
Top: Warm the mashed potatoes with a splash of milk, spread over the filling from the edges in, make fork ridges, add cheddar, and brush with butter.
Bake: Bake 20 to 25 minutes, until bubbling and golden. Rest 10 minutes before serving.