For the dough, pulse-process flour, butter, salt and sugar in food processor and stream in eggs. Knead dough, wrap in plastic and chill for 1 hour.
To make the filling, heat a skillet over medium-high; add oil, 2 turns of the pan. Add chicken and brown and crumble then add garlic and spices, and stir to combine. Add currants and deglaze pan with Calvados; remove mixture to a bowl.