Form the ground beef into 4 equal patties, seasoning with salt and pepper.
Heat olive oil in a skillet over medium-high heat. Cook the patties for 3-4 minutes on each side, until desired doneness is reached.
If using, place a slice of cheddar cheese on each patty during the last minute of cooking and cover the skillet to melt the cheese.
Toast the burger buns lightly on a separate pan or in the oven.
Spread truffle mousse on the inside of each bun. Assemble the burgers by placing the cooked patties on the bun bottom, followed by arugula and the bun top.
Notes
For an extra touch of luxury, add a drizzle of truffle oil over the finished burger.