Preheat the oven to 375ºF.
Heat a Dutch oven over medium-high heat and add the butter.
Add the ham and brown lightly, then add the onions, carrots, celery, and mushrooms. Sauté until the vegetables soften slightly.
Press one of the pie crusts into a pie dish. Make several holes with a fork and bake for about 10 minutes or until just beginning to brown. Reserve.
Add the potatoes, peas, thyme, and stock, and bring to a boil.
Combine the cornstarch with 3 tablespoons of water and whisk into the ham mixture to thicken.
Stir in the cream and remove from the heat.
Place the ham and vegetable mixture into the par-baked pie shell and top with the remaining shell, crimping the edges to seal and cutting a few vents in the top.
Bake for about 40-45 minutes or until golden brown.
Remove from the oven and allow to rest for about 5 minutes. Serve warm.