Preheat oven to 375 degrees F (190 degrees C). Lightly grease a baking sheet, or use parchment paper.
In a large bowl, combine flour, brown sugar, baking powder, salt and cream of tartar. Cut in shortening until mixture resembles coarse crumbs. Mix in milk and vanilla. Knead briefly on a floured surface. Roll out into a large rectangle, 1/2 inch thick. Spread softened butter onto surface of dough. Mix together brown sugar and cinnamon; sprinkle evenly over butter. Roll tightly, and cut into 12 equal slices. Place on prepared baking sheet.
Bake in preheated oven for 15 to 20 minutes, or until golden brown.