In a small bowl, whisk together 1/2 cup mayonnaise, 2 tsp Dijon mustard, 2 tbsp sweet pickle relish, 1 tsp apple cider vinegar, 1/2 tsp hot sauce (if using), 1/4 tsp kosher salt and 1/4 tsp freshly ground black pepper until smooth. Taste and adjust seasoning. Refrigerate while preparing other components to let flavors meld (at least 10 minutes).

Coleslaw

Prepare slaw

In a medium bowl combine 3 cups finely shredded green cabbage, 1 cup shredded red cabbage and 1/2 cup grated carrot. In a separate small bowl whisk 1/4 cup mayonnaise, 1 tbsp apple cider vinegar, 1 tsp sugar, 1/2 tsp Dijon mustard, 1/2 tsp kosher salt and 1/4 tsp freshly ground black pepper until smooth. Pour dressing over the cabbage mixture and toss to coat evenly. Taste and adjust salt or vinegar. Refrigerate for at least 15 minutes to soften the cabbage slightly; drain any excess liquid before assembling if needed.

Sandwich Assembly & Toasting

Assemble sandwiches

Lay out 4 slices of rye bread. Spread about 1 tablespoon of secret sauce evenly over each slice (reserve remaining sauce for serving). On each sauced slice pile approximately 4 ounces (about 1/4 lb) of thinly sliced corned beef, distributing evenly across the 4 sandwiches. Top the corned beef with two slices of Gruyère per sandwich (or enough to cover). Spoon a generous 1/4 to 1/3 cup of the prepared coleslaw onto two of the sandwiches (this recipe layers coleslaw inside; for a milder effect use less). Close with the remaining bread slices, sauce side down.

Butter and toast

Heat a large skillet or griddle over medium-low to medium heat. Butter the outside of each sandwich with about 1 tablespoon softened butter per side (total ~4 tbsp for all sandwiches). Place sandwiches in the skillet, press gently with a spatula or a heavy pan, and cook 3–4 minutes per side until bread is deeply golden brown and Gruyère has melted. If the bread browns before the cheese melts, lower the heat and cover the pan for a minute to help the cheese melt through.

Serve

Transfer sandwiches to a cutting board, let rest 1 minute, then slice in half on the diagonal. Serve hot with extra secret sauce on the side and pickles if desired.