- In the blending cup of an immersion blender, combine the arugula, garlic, pine nuts, cheese, lemon juice, the 3/4 teaspoon salt and 3/4 teaspoon pepper and blend until coarsely chopped, about 30 seconds. While blending, slowly stream in the 3/4 cup olive oil and blend until smooth, about 1 minute. Set the pesto aside.
- Preheat one side of an electric indoor grill to 375ºF and the other side to 400ºF.
- Using your fingertips, loosen the skin on each chicken breast to create a small pocket. Spoon 2 teaspoons pesto into each pocket, then gently spread out the pesto with your fingertips. Grill the chicken, skin side down, over 400ºF heat for 6 minutes. Grill the chicken, skin side down, over 400ºF heat for 6 minutes. Rotate the chicken 180 degrees and grill until the skin is golden brown and crisp, about 5 minutes more. Turn the chicken over and grill, rotating as needed to ensure even browning, until an instant-read thermometer inserted into the thickest part of a breast registers 160ºF, 12 to 14 minutes more.
- Meanwhile, in a bowl, stir together the potatoes, the 3 tablespoons olive oil, salt and pepper. Grill the potatoes, cut side down, over 375ºF heat for 9 to 15 minutes, rotating them every 4 minutes.
- Serve the chicken with the potatoes and pass the remaining pesto alongside.