Prep the pan: Preheat oven to 350°F (175°C). Grease and line a 9×13-inch cake pan with parchment paper.
Mix the dry ingredients: In a medium bowl, whisk together flour, chai spice blend, baking powder, baking soda, and salt. Set aside.
Cream the butter and sugars: In a large mixing bowl, beat butter, granulated sugar, and brown sugar until light and fluffy (2–3 minutes). Add eggs one at a time, mixing well after each. Beat in vanilla.
Finish the batter: Add dry ingredients in three additions, alternating with milk and sour cream, beginning and ending with the dry ingredients. Mix until just combined—do not overmix.
Bake: Spread batter evenly in the prepared pan. Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely before frosting.
Make the buttercream: Dissolve espresso powder in hot water or milk. In a large bowl, beat butter until creamy. Gradually add powdered sugar, mixing on low to combine. Add espresso mixture, vanilla, and salt, then beat on high for 2–3 minutes until fluffy.
Frost: Spread buttercream evenly over the cooled cake. Slice and serve.