Pat fillets dry. Season with salt and white pepper. Dip in oil and butter. Lightly flour fish, shaking off excess and sear until golden brown on each side. Remove fish to warm oven.
In fat flounder was browned in, add shallots, tarragon and crimini mushrooms. Brown lightly. Add lobster claw and knuckle meat. Deglaze with sauvignon blanc. Reduce au sec. Add cream. Reduce by half. Finish with raw unsalted butter, whisking in a little at a time until each piece is absorbed. Serve over flounder.