Combine Jarlsberg cheese, wine, garlic, and pepper in the bowl of a food processor. Process until the mixture is smooth.
The sandwiches
Brush one side of each piece of bread with olive oil (the oil-brushed side will be on the outside of the sandwich).
Spread 1 tablespoon of the Jarlsberg mixture on each slice of bread (2 tablespoons per sandwich).
Divide ham, tomato slices, and arugula leaves evenly over 4 slices of bread. Close each sandwich with a remaining slice of bread.
Heat a large cast-iron skillet over medium to medium-high heat. Place sandwiches in skillet (cook in two batches, if necessary) and cook until cheese is melted and bread is golden brown. Serve.
Notes
Use a dry white wine, such as Sauvignon Blanc, Pinot Gris or Chenin Blanc.Please note that I am not a medical or nutritional professional. I provide nutritional information for my recipes as a courtesy to my readers. It is calculated using the built-in recipe card calculator. While I attempt to provide information that is as accurate as possible, you should calculate the nutritional information independently before relying on it.