Preheat oven to 350 degrees. Grease a 9x13 inch pan and set aside.
Mix together flour, cream of tartar, baking powder, and salt. Set aside.
In a large bowl, cream together butter, granulated sugar, and brown sugar. Whisk until light and fluffy.
Mix in eggs and vanilla extract, mixing well after each addition.
Add 1/3 of the dry ingredients and mix well. Continue with remaining dry ingreditiens until fully combined.
Make the cinnamon sugar by stirring together 1/4 cup granulated sugar and 1 tablespoon cinnamon.
Pour half of the snickerdoodle dough into the prepared baking dish.
Sprinkle half of the cinnamon sugar over the snickerdoodle bar dough.
Scoop the remaining dough and arrange it over the cinnamon sugar.
Slowly spread it out using the back of a spoon until it covers the cinnamon sugar and is in an even layer.
Top with remaining cinnamon sugar.
Bake for 25 minutes, until a toothpick inserted in the center of the snickerdoodle bars comes out clean.
Let fully cool.
Mix together powdered sugar and milk to create a glaze and drizzle over the cooled snickerdoodle bars.
Cut into squares and enjoy.