Make the bread
Position a rack in the lower third of the oven and heat the oven to 350°F. Butter and then flour the bottom and sides of a 6-cup (8-1/2 x 4-1/2-inch or 9 x 5-inch) loaf pan, tapping out any excess flour.
In a large bowl, combine the flour, sugar, baking powder, salt, cinnamon, ginger, and cardamom. Whisk until well blended. Stir in the dried currants.
In a medium bowl, combine the milk, eggs, orange zest, and vanilla. Add the carrots and whisk until blended. Pour the wet ingredients over the dry ingredients. Add the melted butter. Using a silicone spatula, gently fold until blended.
Scrape the batter into the prepared pan and spread evenly.
Bake, rotating halfway through, until the top is golden and a wooden skewer or toothpick inserted in the center comes out clean, 50 to 55 minutes.
Let cool in the pan on a rack for 30 minutes. Invert the bread and remove the pan, turn the bread right side up, and let cool completely.
Glaze the bread
In a small bowl, stir the confectioners’ sugar and the cream until smooth, adding more cream, 1 tsp. at a time, until the glaze is just pourable. Drizzle the bread with the glaze and let it set for 30 minutes. Store, covered, at room temperature for up to 2 days.