Ingredients
1 1/2 sticks unsalted butter, softened, plus more for pan
1 1/2 cups unbleached all-purpose flour
1 1/4 teaspoons baking powder
1/4 teaspoon baking soda
1/2 teaspoon ground cinnamon
1/2 teaspoon ground cardamom
1/2 teaspoon ground ginger
1/2 teaspoon kosher salt (we use Diamond Crystal)
1/2 cup packed light-brown sugar
1/2 cup granulated sugar
2 large eggs, room temperature
1 1/2 teaspoons pure vanilla extract
1/3 cup carrot juice (store-bought or fresh) or water
2 cups shredded peeled carrots (from 1 pound)
3 tablespoons poppy seeds, plus more for sprinkling
1 1/2 cups confectioners' sugar, sifted
3 to 4 tablespoons fresh Meyer-lemon juice
Preparation
For the Cake: Preheat oven to 350°F. Butter a standard loaf pan (8 by 4 inches) and line with parchment, leaving an overhang on both long sides; butter parchment. Whisk together flour, baking powder, baking soda, cinnamon, cardamom, ginger, and salt until combined. Beat butter and both sugars with a mixer on medium speed until pale and fluffy. Add eggs, one at a time, beating well after each addition, then beat 3 minutes more. Add vanilla, carrot juice, and carrots; beat until well combined, about 2 minutes. Reduce speed to low, add flour mixture, then beat in poppy seeds just until combined.
Transfer batter to prepared pan, smoothing top with an offset spatula. Bake until a tester inserted in center comes out clean, about 1 hour. Let cool 20 minutes in pan on a wire rack set inside a baking sheet. Remove cake using parchment, transfer directly to rack, and let cool completely.
For the Glaze: In a large bowl, whisk together confectioners’ sugar and 3 tablespoons lemon juice until smooth, adding more lemon juice, teaspoon at a time, until icing is thick and pourable. Pour glaze over top.
Sprinkle cake generously with poppy seeds and let glaze set completely, about 30 minutes; transfer to a serving platter. Cake can be stored, covered, at room temperature up to 3 days.
