Toast sourdough.
Place Potatoes onto a sizzle platter. Heat in a 500°F oven until heated through, about 3 minutes.
In a small nonstick saute pan over medium heat, add melted butter.
Carefully crack eggs into the pan. Cook until the whites begin to set, about 2 minutes.
Gently break the yolks. Season with S&P.
Carefully flip the eggs. Continue cooking until eggs are over-medium.
Shingle cheese evenly over the eggs. Continue cooking until eggs are over-hard and the cheese is melted.
Spread Peppercorn Aioli evenly over each slice of toast, ensuring coast-to-coast coverage over both.
Lay eggs across the bottom slice.
Shingle Bacon evenly over the eggs. Close the sandwich.
Cut sandwich in half on a slight bias. Place along the front edge of the plate, with cut sides facing out, as shown in the photo.
Place Potatoes on the top left corner of the plate, as shown in the photo.
In a stainless-steel bowl, gently toss arugula with Dijon Balsamic Vinaigrette. Season with S&P. Taste and adjust seasoning as needed.
Build arugula salad on the top right corner of the plate, as shown in the photo.