How to Make It
Place a baking sheet in oven and preheat to 400°F.
Combine basil, parsley, garlic, pepper, 5 tablespoons oil, and 3/4 teaspoon salt in a food processor; process until smooth. Transfer to a large bowl, add chicken and arugula, and toss to coat.
Divide dough into 4 equal portions. Roll each into a 4-by-6-inch oval on a floured surface. Brush with remaining 1 tablespoon oil and season with remaining 1/4 teaspoon salt. Place dough on preheated baking sheet and bake until golden, about 12 minutes. Transfer sheet to a rack and cover with a clean, damp kitchen towel until dough is pliable, about 3 minutes.
Top dough with chicken mixture and cheese and fold in half.