In a small bowl, whisk together mayonnaise, pickle relish, ketchup, horseradish, lemon juice, and Worcestershire. Season with salt and pepper.

In a large skillet over medium-high heat, toast caraway seeds, stirring, until fragrant, about 30 seconds. Transfer to a plate.

Return skillet to medium-high heat and heat oil. Add onion and cook stirring until lightly golden, about 3 minutes. Add the cabbage and carrot and season with salt and pepper. Cook, stirring occasionally, until cabbage is crisp-tender, 5 minutes.

Stir in corned beef and sauerkraut, tossing until warmed throughout, 1 minute more. Top cabbage mixture with Swiss cheese, cover, and cook until cheese is melty and bubbly, 3 minutes. Remove from heat.

Scatter roasted caraway seeds and cornichon on top, then drizzle with dressing and garnish with green onion before serving.