In a saucepan of salted boiling water, cook the wild rice until very tender, about 45 minutes; drain.
Preheat the oven to 475°. Melt the butter in the oil in an enameled cast-iron casserole. Add the shallots and thyme, season with salt and pepper and cook over high heat, stirring, for 2 minutes. Stir in the white and shiitake mushrooms. Bake for about 15 minutes, or until the mushrooms are just wilted. Stir and bake for about 10 more minutes, or until the mushrooms are dry.
In a large measuring cup, combine the skim and whole milk. In a small bowl, gradually whisk 1/4 cup of the milk into the arrowroot until smooth.
Set the casserole over high heat. Add the remaining milk and bring to a boil. Stir in the arrowroot mixture and cook until thickened, about 1 minute. Add the rice and cook, stirring, until heated through. Add the parsley and chives; season with salt and pepper.
One Serving Calories 250 kcal, Cholesterol 9 mg, Total Fat 4 gm, Saturated Fat 1.7 gm.