Lightly brush grill rack with vegetable oil. Then prepare grill with hot coals, or heat gas grill (see Note for Oven Method). Keep coals banked high.
Combine pumpkin seeds, artichoke hearts, jalapeno, garlic, lemon juice, cilantro and 1 tablespoon oil in food processor or blender. Process until uniformly and finely chopped. Season the mole with 1/4 teaspoon salt.
Coat chicken breast halves with the 2 tablespoons remaining oil. Season with the remaining salt and the pepper. Place the chicken between sheets of plastic wrap and pound with a smooth-sided meat pounder or the bottom of a large heavy skillet to 1/8-inch thickness. Remove the plastic wrap from the chicken.
Grill breasts as close to hot fire as possible for 1 minute per side or until browned and no longer pink in the center. Top each breast with several tablespoons of the artichoke mole.
Heat broiler. Coat broiler-pan rack with nonstick vegetable oil. Place the flattened chicken breasts on pan and broil for 2 minutes per side or until browned and no longer pink in the center.