In a medium bowl, whisk together the oil, lemon zest, lemon juice, garlic, cumin, salt, and pepper flakes until smooth. Add the chicken and toss until coated with the marinade. Cover and refrigerate for at least 4 hours or overnight. (Can also be made in a re-sealable plastic bag)
In a food processor, blend the mint, spinach, cheese, walnuts, lemon juice, garlic, salt, and pepper until chunky. With the machine running, slowly add the olive oil until smooth.
Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Spray the grill lightly with vegetable oil cooking spray.
Remove the chicken from the marinade. Discard the marinade. Grill the chicken for 4 to 5 minutes on each side until cooked through. Place on a platter and serve with the pesto.