If desired, caramelize the onions by heating 1 tablespoon of butter in a skillet over medium heat. Add thinly sliced onions and cook, stirring occasionally, until golden brown, about 20-25 minutes. Set aside.

Spread one side of each slice of sourdough bread with softened butter. Flip the slices over and spread the other side with Dijon mustard or Russian dressing.

On 4 slices of bread (dressing side up), layer 2 slices of Muenster cheese.

Add a generous portion of corned beef on top of the cheese.

If using, add a layer of caramelized onions and sauerkraut.

Top with another slice of Muenster cheese.

Place the remaining 4 slices of bread on top, buttered side up.

Using a Panini Press: Preheat the panini press according to the manufacturer's instructions. Place the assembled sandwiches in the press and cook until the bread is golden brown and the cheese is melted, about 3-4 minutes.

Using a Skillet: Heat a large nonstick or cast-iron skillet over medium heat. Place the sandwiches in the skillet and cook, pressing down with a spatula or another heavy skillet, until the first side is golden brown and the cheese starts to melt, about 3-4 minutes. Carefully flip the sandwiches and cook the other side until golden brown and the cheese is fully melted, another 3-4 minutes.

Remove the panini from the press or skillet and let them cool slightly. Cut each panini in half and serve with deli pickles and potato chips on the side.