In a microwave-safe bowl, combine glutinous rice flour, granulated sugar, and milk until smooth. Cover with a damp cloth and microwave for 1 minute; stir, cover again, and microwave for an additional minute to form the mochi center.

Stir in coconut oil while mochi is warm. Allow the mixture to cool for at least 10 minutes.

Grind Thai tea leaves to a fine powder. Heat milk until steaming, then steep the ground tea for about 5 minutes.

In a separate bowl, whisk together all-purpose flour, baking powder, and kosher salt.

In a large bowl, mix melted butter and granulated sugar until creamy. Add in eggs and vanilla extract, followed by the steeped Thai tea mixture, stirring until fully combined. Gradually fold in the dry ingredients.

Cover the cookie dough with plastic wrap and refrigerate for at least 2 hours.

Preheat your oven to 350°F (180°C). Divide the chilled dough, flatten each piece, add a dollop of mochi, then roll into balls.

Roll each cookie ball in granulated and powdered sugar. Place on a baking sheet and bake for 12-15 minutes. Cool on wire racks.