Toss arugula, olive oil, salt and pepper together in a medium bowl. Set aside until ready to use.
Heat a large skillet over medium heat.
Divide the softened butter between the four slices of bread, spreading evenly onto one side of each slice.
Once the skillet is hot, place one slice of bread (butter side down) into the skillet. Immediately sprinkle 1/4 cup of shredded cheddar across the top side of the bread.
Lay three slices of bacon across the cheddar.
Top the bacon with half of the prepared arugula.
Sprinkle another 1/4 cup of shredded cheddar across the arugula. Place another slice of bread (butter side UP) onto the arugula. Gently press down on the sandwich with a spatula.
Cook the grilled cheese 3-4 minutes until browned on the bottom. Carefully flip, and cook another 2-3 minutes until browned and cheese is melted.
Repeat with remaining ingredients to make second sandwich. Slice both in half, and serve hot!
Notes
*Bread: You can also use French, Italian, or any sliced white bread!**Bacon: My favorite method for cooking bacon is in the oven at 375 until crispy (about 15 minutes.) I like to place it on a rimmed baking sheet lined with foil or an oven-safe wire rack.***Apple: Can also use red delicious, or your favorite!