Whisk 3 1/2 cups flour, 1 cup sugar, cream of tartar, and baking soda together in a bowl. Mix vegetable shortening, milk, egg, and vanilla extract into dry ingredients to make a dough. Roll the dough out 1/4-inch thick on a floured work surface. Cut dough into 2 1/2-inch rounds using a biscuit cutter or glass.
Combine raisins, 1/2 cup sugar, and 1 tablespoon flour in a bowl; stir to coat raisins. Spoon 1 rounded teaspoon of raisin mixture into center of a cookie round and top with another round. Use a fork to crimp the edges together to make little pies. Place cookies onto a baking sheet.
Bake in the preheated oven until cookies are lightly golden brown, about 11 minutes. Watch carefully to prevent burning.
Gather cut scraps of dough, gently form into a ball, and roll out again. Repeat steps as before until all dough and filling are used up.
