If the currants are very dry, steam them for 10 minutes.
In a mixer, cream together the butter and sugar at medium speed until light and smooth, about 3 minutes. Add flour, salt, currants, and ginger, and mix until well blended, about 3 minutes. Gather dough into a ball and flatten slightly.
Lightly flour a piece of parchment paper (or use a nonstick baking mat). Place dough on paper or mat and roll out into a 10 inch square, an even 1/4 inch thick. Cover with a towel or plastic wrap and refrigerate until firm, about 1 hour.
Preheat oven to 350 degrees F. Line two cookie sheets with parchment paper. Using a sharp knife, cut dough into 10 1 inch wide strips. Cut each strip into 1-1/2 inch long rectangles. Gather and roll out scraps and cut out more cookies.
One sheet at a time, bake until edges are lightly golden, 12 to 15 minutes. Cool on sheets 5 minutes, then transfer to a rack and cool completely before storing in an airthight container up to 1 week.