Preheat the oven to 350°F (175°C) and line a muffin tin with cupcake liners.
In a small saucepan, melt the butter over medium heat, stirring until it turns golden brown and has a nutty aroma. Let it cool slightly.
In a medium bowl, whisk together the flour, sugar, baking powder, chai spice mix, and salt.
In another bowl, whisk the brown butter with eggs and buttermilk until smooth.
Pour the wet ingredients into the dry ingredients and gently fold until just combined.
Divide the batter evenly among the cupcake liners, filling each about 2/3 full.
Bake for 18-20 minutes, until a toothpick comes out clean. Let cool for 5 minutes before transferring to a wire rack.
Prepare the frosting using butter, powdered sugar, chai spices, and milk for consistency, and swirl it on top of the cooled cupcakes.