Preheat oven to 450 degrees F.
In a shallow baking pan drizzle oil over shiitakes, and toss to coat. Roast mushrooms, stirring once or twice, 12 to 15 minutes, or until golden. Keep oven at 450 degrees. Blanch onions in boiling salted water 1 minute. Drain in a colander and rinse under cold running water to stop cooking. Trim root ends and peel.
Mince roasted shiitake and in a shallow bowl stir together with bread crumbs and salt and pepper to taste. Have ready in separate shallow bowls seasoned flour and egg.
Working with 1 chicken breast at a time, dredge in flour, shaking off excess, and dip in egg, letting excess drip off. Coat chicken with mushroom mixture, gently knocking off excess, and transfer to a plate. Chicken may be prepared up to this point 2 hours ahead and chilled, uncovered, on a rack.
In a 12-inch non-stick skillet heat oil over moderately high heat oil over moderately high heat until hot but not smoking and saute chicken until golden, about 1 minute on each side. Transfer chicken with tongs to baking pan. Scatter pearl onions around chicken and roast in middle of oven 10 minutes, or until chicken is just cooked through.
Cut asparagus diagonally into 2-inch lengths. Arrange on a steamer rack and sprinkle with kosher salt. Steam asparagus, covered, over boiling water until crisp-tender, about 5 minutes, then transfer to a bowl of ice water to stop cooking. Saute shiitakes in 1 tablespoon olive oil. Set aside.
Transfer chicken to a platter, cover loosely with foil. Transfer onions and pan juices to 2 separate small bowls (do not clean roasting pan). To a large skillet add 1 tablespoon butter and cook shiitakes. Saute until mushrooms are softened and browned lightly. Add wine and chicken stock and remaining pan juices and boil until liquid is reduced to about 1/3 cup. Add asparagus and onions.
Cut remaining 2 tablespoons butter into pieces and add to vegetables. Cook over moderately high heat, shaking pan, until butter is just incorporated and vegetables are glazed. Season vegetables with salt and pepper and spoon around chicken.