Whisk flour and salt together in a large bowl; cut in the shortening with a knife or pastry blender until the mixture resembles coarse crumbs. Add ice water, 1 tablespoon at a time, tossing with a fork, until the flour mixture is moistened. When you squeeze a handful of the moistened pastry mixture, it should form a ball. Divide dough in half and shape into balls.
Preheat oven to 450 degrees F (230 degrees C). Spray 36 muffin cups with cooking spray.
Roll pastry out 1/8-inch thick on a lightly floured surface. Cut into 4-inch rounds; press rounds into the bottom and up sides of muffin cups to make tart shells.
Beat brown sugar and butter together with an electric mixer until smooth and creamy; beat in eggs, milk, and vanilla extract just until combined. Stir raisins and currants into butter mixture; fill tart shells with mixture 2/3-full.
Bake in the preheated oven for 8 minutes; leaving oven closed, reduce temperature to 350 degrees F (180 degrees C) and bake until filling is bubbly and pastry is lightly browned, about 15 minutes.