Make chai spice: In a bowl, mix all spices together. Store leftovers in an airtight jar for up to one year.

Brown butter: Melt butter in a skillet over medium heat until foamy and golden with a nutty aroma. Cool to room temperature.

Cream butter and sugars: In a mixing bowl, beat browned butter with granulated and brown sugars until smooth. Add eggs and vanilla, and beat 2–4 minutes until pale and fluffy.

Combine dry ingredients: In a separate bowl, whisk flour, chai spice blend, baking soda, and salt. Slowly add to wet mixture and stir until just combined. Dough will be soft and slightly sticky.

Prepare topping: In a small bowl, mix sugar and chai spice blend.

Chill dough: Scoop 3‑tbsp portions, roll into balls, and coat in chai sugar. Chill at least 2 hours or overnight.

Bake: Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper and space cookies 2–3 inches apart. Bake 9–11 minutes until edges are set and centers soft. Cool on sheet 2–3 minutes, then transfer to a wire rack.

Add glaze: Whisk powdered sugar and vanilla bean paste, slowly adding milk until thick but drizzle‑ready. Pipe or drizzle over cooled cookies.