Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Cream the butter and sugar
In a large mixing bowl, combine the butter, vegetable oil, and granulated sugar. Beat until smooth and well blended.
Incorporate wet ingredients
Add the egg, vanilla extract, powdered sugar, and chai tea leaves. Mix until evenly combined.
Combine dry ingredients
In a separate bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg. Gradually fold the dry ingredients into the wet mixture until a soft dough forms.
Chill the dough
Cover the bowl with plastic wrap and refrigerate for 1 hour to allow the dough to firm up.
Shape and bake
Scoop approximately 1 tablespoon of dough per cookie and place evenly on the prepared baking sheet. Gently flatten each portion and sprinkle with sugar. Bake for 9–12 minutes, or until the edges are lightly golden. Allow cookies to cool completely on a wire rack.
Prepare the glaze
In a small bowl, whisk together powdered sugar, milk, cinnamon, and chai tea leaves until smooth. Adjust the consistency by adding additional milk (for a thinner glaze) or powdered sugar (for a thicker glaze).
Glaze and serve
Once cookies have cooled, drizzle with the chai glaze. Allow the glaze to set before serving.
Notes
To make these cookies gluten free, substitute the all-purpose flour with a certified 1:1 gluten-free flour blend. Ensure the chai tea and powdered sugar are labeled gluten free, as some brands may process with gluten-containing ingredients.