Rinse rabbit and pat dry. Sprinkle rabbit pieces with salt, then dust with flour. Melt 5 to 6 Tbsp of the butter in a wide frying pan over medium-high heat. Add rabbit, a few pieces at a time (do not crowd pan); cook, turning as needed, until browned on all sides.
Transfer rabbit to a shallow 3 1/2 to 4-quart baking pan. Move frying pan into an open area, away from exhaust fans and flammable items. Add brandy and ignite; shake or tilt pan until flame dies. Pour brandy mixture over rabbit in baking pan; set aside.
Melt remaining 2 to 3 Tbsp butter in frying pan over medium heat. Add onions, minced parsley, and mushrooms; cook, stirring often, until onions are soft, about 5 minutes. Stir in mustard, cream, and lemon juice and bring to a boil. Pour sauce over rabbit. Cover and bake in a 375° F oven until rabbit is tender when pierced, about 45 to 55 minutes.
Drain cooking liquid into a wide frying pan and bring to a boil; boil for 1 minute. Beat some of the hot liquid into egg yolks, then return yolk mixture to pan. Cook, stirring constantly, until sauce is thickened; do not boil. Season to taste with salt. Transfer rabbit to a serving dish. Pour sauce over rabbit and sprinkle with chopped parsley. Serve.
Servings: 6 to 8