Preheat oven to 350 degrees. Butter 6 cups of a jumbo muffin tin (each cup should have a 1-cup capacity). Heat currants and 1 cup water in a small saucepan over low heat until currants are plump, about 20 minutes. Drain; let currants cool.
Whisk together flour, baking powder, baking soda, salt, cardamom, and ginger in a medium bowl; set aside.
Put eggs, oil, and sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until combined. Reduce speed to low. Add the flour mixture in three batches, and mix until just combined after each addition. Fold in the carrots and currants.
Pour batter into prepared muffin tin, leaving a 1/2-inch space above batter in each cup. Bake until tops are golden and a cake tester inserted into centers comes out clean, about 30 minutes. Let muffins cool in tin on a wire rack for 10 minutes.
Remove tin from rack, and lightly oil rack. Run a thin knife around the sides of muffins to loosen, and unmold. Let cool completely on rack.
Muffins can be stored in an airtight container at room temperature, up to 2 days.