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, followed by apple slices to cover the whole slice of bread.
Lay three slices of bacon across the cheddar, then 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! Line a large rimmed baking sheet with foil or parchment paper, lay the bacon strips in a single layer on top, then cook the bacon at 375º F until crispy (about 18-20 minutes, depending on thickness.) ***Apple: Can also use red delicious, or your favorite apple!