Combine kale, 1 tablespoon oil, salt, and pepper in a large zip-top heavy-duty plastic bag; seal bag, and shake to coat. Remove kale from bag, and place in a wire grilling basket coated with cooking spray. Prepare grill. Place grill basket on grill rack, and grill 5 minutes on each side or until kale begins to char around edges.
Place kale in a large bowl. Combine remaining oil and vinegar; stir well with a wire whisk. Pour vinegar mixture over kale; toss well. Serve kale immediately.