Microwave limes for about 30 seconds to release essential oils, and set aside just long enough so that they are cool enough to handle.
Turn on the blender and while it's running, add 1 at a time through the feed tube, the parsley, chives, and garlic, and blend together until a smooth paste has formed. At this point the limes should be cool enough to squeeze. With the power still on, squeeze the lime juice through the blender feed-tube, and then very slowly add the buttermilk until the mixture thickens and can coat the back of a spoon. Adjust the seasoning with salt and pepper. Set aside in refrigerator until needed. (When chilled, the dressing should resemble something like mayonnaise.)
Toss together lettuce, spinach, onion, celery, chives, and cucumbers. Fold in peas, corn, pineapple, cranberries, grape tomatoes, and tomato wedges. Serve family style with dressing on the side.