In a small bowl, whisk together the Dijon mustard, raw honey, and black pepper until the glaze is smooth and combined.
Lay out the sourdough slices on a clean surface and spread the honey mustard mixture evenly over one side of each slice.
Layer the lean ham onto one slice of bread, followed by the Swiss cheese and the fresh arugula.
Place the second slice of bread on top, mustard-side down, to close the sandwich.
Lightly brush the outside of the sourdough bread with avocado oil to ensure a golden, crispy exterior.
Heat a panini press or a heavy bottomed skillet over medium heat.
Place the sandwich in the press or skillet, using a second heavy pan to weigh it down if using a skillet.
Grill for 3 to 4 minutes per side until the bread is toasted and the Swiss cheese has reached a gooey, melted consistency.
Remove from heat, slice the panini diagonally, and serve while warm.