Microwave limes for about 30 seconds to release essential oils, and set until cool enough to handle. Turn on the blender and while it's running, add 1 at a time through the feed tube, the parsley, cilantro, garlic, mayonnaise, and mascarpone cheese, and blend together until a smooth paste has formed. At this point, the limes should be cool enough to handle. With the power still on, squeeze the lime juice through the blender feed-tube, and then very slowly add the buttermilk until the mixture can coat the back of a spoon. Adjust the seasoning with salt and pepper. Set aside in refrigerator until needed.
Melt the oil and butter in a saute pan over medium heat and saute the peaches lightly. Set aside to cool.
Bang the core part of the head of lettuce on a hard surface and twist it to remove), cut into 1-inch pieces, rinsed and dried with a salad spinner. To make the bite sized pieces, cut the head of lettuce in half then with flat sides against cutting board, cut into 1-inch strips lengthwise and then 1-inch squares crosswise.
Toss together iceberg lettuce, romaine lettuce, fresh ginger, and cucumbers. Fold in tomato wedges and cooled peaches, and crumble in blue cheese. Transfer to serving dishes and serve with buttermilk dressing on the side.