Stir together the flour, granulated sugar, baking powder, soda, cream of tartar, and salt.
Cut in shortening till mixture resembles coarse crumbs.
Stir in pecans.
Combine egg and buttermilk; add all at once to dry mixture.
Stir just till dough clings together.
Knead gently on lightly floured surface (10 to 12 strokes).
Roll to 15x10-inch rectangle.
Brush with melted butter.
Cut crosswise into ten 10 x 1 1/2 inch strips.
Make 2 stacks of 5 strips each.
Cut each stack into 6 pieces.
Place biscuits, cut side down, in greased muffin pans.
Bake at 400° about 22 minutes.
Meanwhile, in small bowl combine the powdered sugar and vanilla.
Stir in enough milk (about 1 1/2 teaspoons) till of drizzling consistency.
Drizzle over warm biscuits