Spread each of 4 slices of bread with 1/2 tablespoon of butter. Now spread each with 1 tablespoon of the apple butter. Top each slice of bread with a couple of slices of turkey, cover that with 2 to 3 slices of brie (enough to cover the turkey), and finally, arrange 2 to 3 arugula leaves on top. Spread the remaining 4 bread slices with 1/2 tablespoon of butter and lay them, buttered sides down, over the cheese; press gently.
Heat a large cast-iron or other heavy skillet over medium-low heat. Add the remaining 1 tablespoon butter and let it melt to evenly coat the bottom of the pan. Add as many sandwiches as will comfortably fit (either 2 or 4) and cook 2 to 3 minutes until the bread is golden brown and the cheese begins to melt. Flip and cook 2 to 3 more minutes to brown the bread. (Add another tablespoon of butter and cook the remaining sandwiches, if you need to.) Cut the sandwiches in half and serve hot.
Recipe courtesy of Tyler Florence