In a small bowl, combine the mayonnaise, cranberries and mustard. Cover and refrigerate.
In another bowl, combine the egg, cheese, pecans, bread crumbs, onions, mustard, tarragon, salt and pepper. Crumble chicken over mixture and mix well. Shape into 12 patties. Chill.
For biscuits, in a small bowl, combine the flour, baking powder and salt. Cut in shortening until mixture resembles coarse crumbs. Stir in milk just until moistened. Stir in cheese and pecans. Turn onto a lightly floured surface; knead 8-10 times.
Pat or roll out to a 12x4-in. rectangle; cut into twelve 2-in. square biscuits. Place 2 in. apart on an ungreased baking sheet. Bake at 450° for 8-12 minutes or until golden brown.
Meanwhile, in a large skillet, cook chicken patties in oil over medium heat for 2-4 minutes on each side or until a thermometer reads 165° and juices run clear.
Slice warm biscuits in half. Spread bottoms with mayonnaise mixture; top with a burger and lettuce. Replace tops.