Step 1

Preheat oven to 500°F (broil).

Step 2

Line a small baking sheet with foil. Put the pepper on the baking sheet and broil until the skin is beginning to char, using tongs to turn occasionally, about 10 minutes. Remove the baking sheet from the oven and wrap the foil around the pepper. (Use oven mitts!) Let the pepper steam in the foil for 10 minutes.

Step 3

Remove the pepper from the foil and transfer it to a cutting board. Peel off the skin, cut off the stem, pull out the seeds, and discard them. Cut the rest of the pepper into thick strips.

Step 4

Spread 1 tablespoon of pesto onto the bottoms of the ciabatta bread. Divide the pepper strips onto the bread, then place the mozzarella slices on top of the pepper strips. Top with the remaining slices of bread and brush the tops with olive oil. (If you're going to serve the sandwiches cold, don't brush them with oil—just eat them!)

Step 5

Heat a grill pan or griddle over medium heat. Flip the sandwiches over and place them on the grill pan oiled-side down, then brush the other side of the sandwich with oil. Use a spatula to press the sandwiches down slightly, but don't press too hard or you'll have a mess of mozzarella everywhere! Cook 5–8 minutes on each side, or until golden brown.

Step 6

Combine arugula, walnut pieces, cheese, and garlic in the large bowl of a food processor. Pulse until finely chopped, then pour olive oil through the feed tube and continue to process until almost smooth. Season with salt and pepper to taste.