- In a non-stick skillet over medium heat, soften the leek in 2 tbsp of the butter for 5 minutes. Add the arugula and cook for 1 minute. Season with salt and pepper. Set aside in a small bowl. Clean out the skillet.
- Spread one side of each slice of bread with the mustard. Divide the leek, cheese and bacon among 4 slices of bread. Close the sandwiches with the remaining bread. Butter the outsides of the sandwiches with the remaining butter.
- In the same skillet over medium-low heat, brown two sandwiches at a time, about 3 minutes per side, pressing the sandwiches down with a spatula until the cheese has melted. Cut the sandwiches in half, if desired.