Begin by preheating your oven to 350°F (175°C). Prepare a 9×9-inch light metal baking pan by greasing it and lining the bottom with parchment paper for easy removal. In a medium-sized bowl, combine the dry ingredients: 2 1/4 cups (282 g) all-purpose flour (spooned and leveled), 1 tablespoon ground cinnamon, 1 1/2 teaspoons ground ginger, 1/2 teaspoon ground allspice, 1/2 teaspoon ground nutmeg, 1 teaspoon ground cardamom, 1/4 teaspoon ground cloves, 1 1/2 teaspoons baking powder, 1/4 teaspoon baking soda, and 1/2 teaspoon salt. Whisk everything together until fully blended, then set the bowl aside.

In a large mixing bowl, add 10 tablespoons (140 g) of softened unsalted butter, 1 cup (200 g) granulated white sugar, and 1/2 cup (110 g) packed brown sugar. Using an electric mixer on high speed, cream the mixture together for about 2 minutes, or until it becomes fluffy and pale. Add in 3 room-temperature eggs, one at a time if preferred, along with 1 tablespoon vanilla extract. Continue mixing on medium speed until the mixture becomes smooth and lighter in color—this should take about 1 minute.

Gradually add the dry ingredients and 1 cup (240 ml) room-temperature buttermilk to the butter mixture, alternating between wet and dry ingredients. Mix on low speed just until everything is combined and the batter is smooth, scraping the sides of the bowl as needed to ensure all ingredients are incorporated. Pour the batter into the prepared baking pan, smoothing the top with a spatula. Bake the cake for 35–38 minutes, or until a toothpick inserted into the center comes out clean. Once baked, let the cake cool in the pan on a wire rack for 30 minutes. Then, carefully lift it out using the parchment paper and transfer to the rack to cool completely.

While the cake is baking, start making the frosting. Place 1 1/4 cups (280 g) of unsalted butter in a large saucepan over medium heat. Melt the butter and let it simmer until it becomes foamy, develops a rich golden brown color, and releases a nutty aroma—this should take around 10–12 minutes. Pour the browned butter into a large bowl and refrigerate until it solidifies but is still soft enough to whip.

Once the brown butter has chilled to the right consistency, beat it on high speed using an electric mixer until it becomes light and fluffy, which should take 5–10 minutes. Next, add 8 oz (226 g) of cold cream cheese and beat on medium speed until the mixture is fully incorporated and smooth. Sift in 2 cups (260 g) of powdered sugar and mix on low speed until the sugar is incorporated. Then increase to high speed and beat for about 1 more minute until the frosting becomes fluffy and spreadable.

As the cake cools, prepare the chai milk soak. In a small saucepan, heat 1/2 cup (120 ml) whole milk over low heat until it begins to steam. Add 2 chai tea bags and steep for 20 minutes. After steeping, discard the tea bags and allow the milk to cool to room temperature. Once cooled, pour the milk into a liquid measuring cup or another container that’s easy to pour from. Stir in 1/2 cup (150 g) sweetened condensed milk and 1 teaspoon vanilla extract. Set the mixture aside until it’s time to assemble the cake.

When the cake has fully cooled, use a sharp knife to slice a very thin layer off the top. This helps the chai milk soak absorb more easily into the sponge. Transfer the cake to your serving plate. Using a wooden stick, skewer, or the handle of a wooden spoon (such as a honey dipper), poke small holes all over the top of the cake. Slowly pour the chai milk soak over the top, allowing it time to seep into the holes and spread evenly through the cake.

Once the soak is fully absorbed, generously frost the top of the cake with the prepared brown butter cream cheese frosting. Use an offset spatula to smooth the frosting into an even layer. Finish with a dusting of ground cinnamon over the top. Slice the cake into 16 equal squares and serve.