Spiced Carrot Cake with Vanilla Bean-Cream Cheese Frosting
The Indian tea called chai inspired this variation.

Follow the recipe for Simple Carrot Cake with Cream Cheese Frosting, substituting an equal amount ground black pepper for the nutmeg, increasing the cloves to ¼ teaspoon, and adding 1 tablespoon ground cardamom along with the spices. For the frosting, using a paring knife, halve and scrape the seeds from 2 vanilla beans and add the seeds to the food processor along with the vanilla extract.

Simple Carrot Cake with Cream Cheese Frosting
Makes one 13 by 9-inch cake
If you like nuts in your cake, stir 1 1/2 cups toasted chopped pecans or walnuts into the batter along with the carrots. Raisins are also a good addition; 1 cup can be added along with the carrots. If you add both nuts and raisins, the cake will need an additional 10 to 12 minutes in the oven.

Carrot cake
2 ½ cups (12 ½ ounces) unbleached all-purpose flour
1 ¼ teaspoons baking powder
1 teaspoon baking soda
1 ¼ teaspoons ground cinnamon
½ teaspoon ground nutmeg
1/8 teaspoon ground cloves
½ teaspoon salt
1 pound (6 to 7 medium) carrots, peeled
1 ½ cups (10 ½ ounces) granulated sugar
½ cup (3 ½ ounces) packed light brown sugar
4 large eggs
1 ½ cups safflower, canola, or vegetable oil

Cream cheese frosting
8 ounces cream cheese, softened but still cool
5 tablespoons unsalted butter, softened but still cool
1 tablespoon sour cream
½ teaspoon vanilla extract
1 ¼ cups (4 ½ ounces) confectioners' sugar

1. For the cake: Adjust an oven rack to the middle position and heat the oven to 350 degrees. Spray a 13 by 9-inch baking pan with nonstick cooking spray. Line the bottom of the pan with parchment and spray the parchment.

2. Whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and salt in a large bowl; set aside.

3. In a food processor fitted with a large shredding disk, shred the carrots (you should have about 3 cups); transfer the carrots to a bowl and set aside. Wipe out the food processor workbowl and fit with the metal blade. Process the granulated and brown sugars and eggs until frothy and thoroughly combined, about 20 seconds. With the machine running, add the oil through the feed tube in a steady stream. Process until the mixture is light in color and well emulsified, about 20 seconds longer. Scrape the mixture into a medium bowl. Stir in the carrots and the dry ingredients until incorporated and no streaks of flour remain. Pour into the prepared pan and bake until a toothpick or skewer inserted into the center of the cake comes out clean, 35 to 40 minutes, rotating the pan halfway through the baking time. Cool the cake to room temperature in the pan on a wire rack, about 2 hours.

4. For the frosting: When the cake is cool, process the cream cheese, butter, sour cream, and vanilla in a clean food processor workbowl until combined, about 5 seconds, scraping down the bowl with a rubber spatula as needed. Add the confectioners' sugar and process until smooth, about 10 seconds.

5. Run a paring knife around the edge of the cake to loosen from the pan. Invert the cake onto a wire rack, peel off the parchment, then invert again onto a serving platter. Using an icing spatula, spread the frosting evenly over the surface of the cake. Cut into squares and serve. (Cover leftovers and refrigerate for up to 3 days.)