Heat the oven to 350°F. Place dried porcini in a small heatproof bowl. Pour boiling water over them and set aside.
Place wild rice in a small saucepan and add enough cold water to cover by 3 inches. Bring to a boil over medium-high heat; cover the pan, leaving the lid slightly ajar; reduce heat; and simmer until rice is almost completely cooked, about 18 to 20 minutes. (The rice will be chewy and swollen with a slightly burst-open appearance.) Drain in a colander and set aside.
While the wild rice simmers, blot chicken thighs and drumsticks dry with a paper towel and season generously with salt and freshly ground black pepper. Heat olive oil in a 12-inch frying pan over medium-high heat. Brown chicken in three batches until golden brown (the chicken will not be fully cooked), about 5 minutes per side, and set aside. Remove the pan from heat and allow to cool for a few minutes. Pour off all but 1 tablespoon of the chicken fat from the pan.
Remove soaked mushrooms from their liquid, reserving the soaking liquid. Coarsely chop the mushrooms and set aside.
Return the frying pan to the stove over medium heat and melt butter. When it foams, add onion and a generous pinch of salt. Stir to coat onion with butter and cook until onion has softened a bit, about 2 minutes, then stir in celery and carrot. Cook, stirring occasionally, until vegetables are slightly softened but still uncooked in the center, about 3 minutes. Season with salt and freshly ground black pepper.
Stir in Arborio rice, mixing well with a wooden spoon or spatula to coat each grain with oil. Cook, stirring occasionally, until the outer layer of the rice becomes translucent and is just beginning to brown, about 4 minutes. Add wine and stir until it evaporates, about 1 minute. Add chopped porcini mushrooms with their soaking liquid and stir until liquid is almost completely evaporated, about 1 minute.
Stir in cooked wild rice and chicken broth and bring to a simmer. Cook, stirring often, until mixture is slightly thickened and rice is about halfway cooked, about 5 minutes (the mixture will be very soupy). Stir in thyme, cream, and sherry, then remove from heat. Taste and if necessary season with more salt and freshly ground black pepper.
Pour mixture into a 13-by-9-inch baking dish. Place chicken pieces over mixture, nestling them close to each other so they will all fit in the dish.
Bake casserole until rice is tender and has absorbed most of the liquid and chicken is completely cooked, about 45 to 50 minutes. To serve, place a scoop of rice mixture on a serving plate and top with a drumstick and thigh.
Beverage pairing: La Crema Sonoma Coast Chardonnay, California. Chicken, mushrooms, and cream just beg for a good, cool-climate Chardonnay. This one garnishes the flavors in the dish with a touch of lemon and pear.
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