In a large bowl, toss greens, tomatoes, cucumbers, carrots and shallots with enough dressing to coat. Sprinkle cubed feta cheese on top.
Microwave lime for about 30 seconds to release essential oils, and set aside to cool.
For the Dressing:
Turn on the blender and while it's running, add 1at a time through the feed tube, the parsley, chives, dill, and garlic, and blend together until a smooth paste has formed. At this point the lime 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 and xanthan gum 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.)