Preheat your oven to 350°F (175°C). Grease a 9x13 inch cake pan with nonstick spray.

In a medium bowl, whisk together flour, chai spice mix, baking powder, baking soda, and a pinch of salt.

In a stand mixer, beat together eggs and granulated sugar for about 1 minute, then add pumpkin puree, melted brown butter, buttermilk, and vanilla extract. Mix until just combined.

Gradually add the dry ingredients to the wet ingredients in the stand mixer. Mix on low speed until just combined.

Pour the batter into the prepared cake pan and smooth the top. Bake for about 35 minutes or until a toothpick comes out clean.

Remove from the oven and allow to cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely.

In a skillet, melt the butter over medium heat, stirring continuously until golden brown, then mix with powdered sugar and a splash of milk until smooth.

Spread the brown butter frosting evenly across the top of the cooled cake.