How to Make It
Preheat oven to 350°F. Stir together 1/3 cup flour, salt, and pepper in a shallow dish. Working with 1 quail at a time, dredge in flour mixture, shaking off excess, and transfer to a baking sheet, placing quail in a single layer. Set aside.
Melt 2 tablespoons butter in a large skillet over medium-high; arrange mushrooms in a single layer, and cook until bottoms are lightly browned, about 4 minutes. Stir and cook, stirring occasionally, until browned all over, about 5 minutes. Transfer mushrooms to a bowl, and set aside.
Return skillet to heat over medium-high. Melt remaining 1/2 cup butter in skillet. Add 3 quail. Cook, swirling skillet occasionally, until quail are lightly browned, 3 to 5 minutes per side. Transfer to a 2-quart baking dish. Repeat with remaining 3 quail.
Add remaining 1/3 cup flour to drippings in skillet. Cook over medium-high, whisking constantly, 1 minute. Gradually whisk in chicken broth and sherry, and return to a simmer. Reduce heat to medium, and whisk until gravy is thickened, about 2 minutes. Stir in mushrooms. Pour gravy over quail; cover dish with aluminum foil, and bake in preheated oven until quail are cooked through and tender, about 1 hour. Divide rice among bowls; top each with 1 quail. Season gravy with salt to taste, and spoon over quail; garnish with parsley and lemon zest.