1. Preheat a grill or grill pan.
2. Put the ground beef in a bowl and season with a generous pinch of salt and pepper. Mix together with your hands to combine. Take a small amount (about 2 tablespoons worth) of the ground beef and roll it in the palm of your hand like you are making meatballs. Flatten the top slightly and put the mini burger patties on a side plate. Drizzle the burgers with oil and season the tops with salt and pepper. Turn the burgers over and season the other side.
3. Place the burgers on the hot grill. Cook for 3 minutes, then turn them over with tongs. Put about 1/2 ounce of aged cheddar cheese on top of the burgers, allowing it to melt. While that's cooking, put the brioche circles on the grill. Let them toast slightly on both sides, about 2 minutes total time.
4. To put the burgers together: Put the toasted brioche circles on a platter. Top each with a small spoonful of Remoulade. Put the burger on top (cheese side up), followed by an arugula leaf, a slice of tomato and a slice of cornichon.

Yield: 6 servings