In a bowl, mix ground chicken, basil, pecorino cheese, bread crumbs, black pepper, egg, and salt until just combined.
Form into burger patties.
Heat a cast iron pan over medium heat with a little oil.
Cook patties for 5-6 minutes per side until golden brown and fully cooked.
Meanwhile, make the lemon mayo: Mix ⅓ cup light mayo, zest of a lemon, and 1 tsp freshly ground black pepper in a small bowl.
Toast burger buns and spread with lemon mayo.
Assemble with thinly sliced tomatoes, arugula, and shaved pecorino.