Line a baking sheet with parchment paper. Whisk together the flour, salt, baking soda, and allspice in a medium bowl. Toss in the currants.
Cream the butter and sugar together in the bowl of a standing mixer fitted with the paddle, until the butter turns a couple of shades lighter. Add the eggs, and mix on a medium speed for 2 minutes. Beat in the sour cream.
Gradually fold in the flour mixture using a rubber spatula. Drop small mounds of dough on the parchment paper – I use an ice-cream scooper for this so they’re all the same size. It doesn’t matter how close they are to each other at this point. Freeze for 2 hours. This will help the cookies to hold their shape instead of completely flattening during baking.
Preheat the oven to 350˚F, and rearrange the cookies onto two baking sheets, at least 1 ½” apart. Bake for 12-14 minutes. Completely cool on a rack before icing.
Note: Feel free to skip the freezing step if you don’t mind thin, flat cookies.