Preheat the oven to 400°F.
Heat 1 tablespoon of the butter in a saucepan over medium heat. Add mushrooms and cook, stirring frequently, until they soften and release their liquid, about 8 minutes. Stir in garlic and cook until fragrant, about 1 minute more. Transfer to a bowl and set aside.
In the same saucepan, melt the remaining tablespoon butter over medium-high heat. Stir in flour, salt and pepper. Gradually add broth and 1 cup of the ricemilk, alternating 1/3 cup of each at a time, whisking constantly. Cook over medium-high heat until mixture comes to a boil and thickens slightly, then remove from the heat. Stir in thawed vegetables, mushrooms and any juices, parsley, thyme, rosemary and celery seed.
Set one of the pie crusts on a rimmed baking sheet to catch any spills. Pour vegetable mixture into the crust, mounding the mixture in the middle. The pie pan will be very full. Invert the second pie crust over the filling, then remove the foil pan. Pinch the edges of both crusts to seal them together. Brush the top with the remaining tablespoon of ricemilk. Cut slits into the top crust so steam can escape. Bake on the baking sheet 35 to 40 minutes, until browned. Let stand 10 minutes before serving.