Heat 3 tablespoons of the butter in a pot over medium heat. Add half the onions and cook until softened, 5–7 minutes. Add 1⁄2 cup of the wine, sauerkraut, and salt and pepper; boil. Reduce heat to medium; simmer, partially covered, 8–10 minutes. Drain the sauerkraut mixture and set aside.
Heat remaining butter in a pot over medium heat. Add remaining onions; cook until softened, 5–7 minutes. Add oyster liquor, remaining wine, 1⁄2 cup cream, and vermouth and bring to a boil. Lower heat to medium-low; reduce by half, about 20 minutes. Remove from heat; whisk in egg yolk and remaining cream. Add cayenne and season with salt and pepper. Set sauce aside.
Heat broiler with rack 4" from element. Divide sauerkraut between shells; top each with an oyster. Spoon some sauce over each and broil until light golden brown, about 5 minutes.