Step 1

Heat the oven to 350°F. Line a 9x13-inch baking pan that’s at least 2 inches tall with parchment paper so the paper hangs over two long sides to form a sling. Coat the paper and pan with cooking spray.

Step 2

Whisk 2 1/4 cups all-purpose flour, 1 tablespoon ground cinnamon, 1 1/2 teaspoons baking powder, 1 teaspoon baking soda, 1 teaspoon ground ginger, 1 teaspoon ground nutmeg, and 1/2 teaspoon ground cloves together in a medium bowl.

Step 3

Beat 1 stick room temperature unsalted butter, 1 1/2 cups granulated sugar, and 1/2 cup packed brown sugar with the paddle attachment in a stand mixer on medium speed until fluffy, about 3 minutes. Beat in 4 room temperature large eggs one at a time, beating well after each addition. Beat in 1/4 cup Greek yogurt, 1 teaspoon vanilla extract, and 1/2 teaspoon kosher salt.

Step 4

Add 1/3 of the flour mixture and beat on low speed until just combined. Beat in 1/2 cup of the whole milk, followed by half of the remaining flour mixture. Beat in the remaining milk and flour mixture, mixing until just combined. Transfer to the pan and smooth out the top.

Step 5

Bake until a tester inserted in the center comes out clean, 30 to 35 minutes. Let the cake cool in the pan for 20 minutes. Grasping the excess parchment, lift the cake slab out of the pan and place on a wire rack. Let cool completely, about 1 hour.

Step 6

Beat 8 ounces room temperature cream cheese and 1 stick unsalted butter with the paddle attachment in a stand mixer on medium speed until combined and fluffy, about 3 minutes.

Step 7

Beat in half of the powdered sugar (about 2 cups) until combined. Beat in the remaining powdered sugar, 1 tablespoon whole milk, and 1 teaspoon vanilla extract on high speed until fluffy, about 3 minutes. Spread onto the spice cake.