Before putting together sandwich, make a plate of arugula and sliced tomatoes and set aside with unsalted butter.
Butter 1 side of each bread slice, then put 4 slices, buttered side down, on a work surface. Top the bread slices with the pancetta, distributing it evenly. Top each with a second slice of bread, buttered side up.
Heat a cast iron skillet or grill pan until hot. Place the sandwiches in the skillet and top with a weight, such as another skillet. Cook until nicely browned, 2 to 3 minutes, then turn the sandwiches and replace the weight. Cook until the second side is well browned, about 2 minutes.
Transfer the sandwiches to a work surface and remove the top slice of bread from each sandwich. Spread the underside of those slices with the basil mayonnaise. Top the pancetta with the tomato slices, pepper to taste, and arugula leaves. Replace the top slice of bread, cut the sandwiches in half, and serve immediately.
Take the roll of pancetta, and dice into about 1-inch cubes. Drizzle some olive oil into a saute pan on medium heat. Add pancetta to heated oil and cook until crispy. Pour the cooked cubes with fat, into a bowl and allow to cool.
Place basil leaves in blender and puree until almost fine. Add mayonnaise to blender and season with freshly ground black pepper, to taste. Puree together until smooth.