Put the wild rice in a fine-mesh sieve and rinse it under cold running water, swishing the rice with your hands until the water runs clear. Transfer the rice to a medium bowl and add water to cover. Pour off any black bits or floating kernels, and then pour the rice back into the sieve to drain.
Cook the rices separately: Combine the wild rice with 1/4 teaspoon salt and 1 cup water in a small saucepan. Bring to a simmer, cover tightly, reduce the heat to low and steam until the rice is tender and curling into a C shape, 20 to 25 minutes.
At the same time, combine the basmati rice, 1/2 teaspoon salt and 1 3/4 cups water in another small saucepan. Bring to a simmer, cover tightly, reduce the heat to low, and steam until the rice is tender, 25 minutes.
Combine the rices in a large bowl and cover tightly.
Cook the vegetable base: Heat the butter in a large skillet over medium heat. Add the celery and onion and cook, stirring often, until the vegetables are limp but still bright, about 10 minutes. Add the garlic and thyme, and cook for 5 minutes.
Pour the vegetables over the rice, scraping the pan for the juices, and stir to combine. Add the pistachios, chestnuts and parsley and mix thoroughly. Serve hot.
Adapted from "The New Midwestern Table" by Amy Thielen (c) Clarkson Potter, 2013. Provided courtesy of Amy Thielen. All rights reserved.