Butterfly the chicken breasts by slicing them horizontally into two thinner pieces.
In a small bowl, mix olive oil, garlic powder, onion powder, smoked paprika, oregano, salt, and black pepper. Brush the chicken with the seasoning mixture on both sides.
Heat a grill or grill pan over medium-high heat. Lightly oil the grates or pan. Grill the chicken for 4–5 minutes per side or until the internal temperature reaches 165°F (74°C). Remove from the grill and let rest for 5 minutes.
In a food processor, combine basil, Parmesan cheese, pine nuts, garlic, olive oil, salt, and pepper. Pulse until smooth, scraping down the sides as needed. Adjust the consistency with a little more olive oil, if necessary.
Slice the ciabatta rolls in half or use sourdough slices. Toast the bread lightly on the grill or in a skillet until golden brown.
Spread a generous layer of pesto on the bottom slice of each piece of bread. Add a grilled chicken piece on top, followed by a slice of cheese. Layer with tomato slices and a handful of arugula. Spread mayonnaise on the top bread slice, if desired, and place it on top to complete the sandwich.
Place the assembled sandwiches back on the grill or in a skillet for 1–2 minutes, covering with a lid, to melt the cheese.
Cut the sandwiches in half and serve warm with chips, salad, or a bowl of soup.