In a bowl, whisk together flour, tea, salt, and spices. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together butter and 1/2 cup sugar until light and fluffy. Mix in the vanilla.
Add the flour mixture in 3 additions, mixing on medium-low speed until just combined. Scrape the bowl between additions.
Turn dough out onto a lightly-floured surface and shape into a rectangle about 1-inch thick. Wrap in plastic wrap and refrigerate for 1 hour.
Preheat oven to 325 degrees F and line a baking sheet with parchment.
Roll chilled dough between two pieces of waxed paper into a 9x10-inch rectangle (about 1/4-inch thick). Cut into 24 rectangular pieces. Transfer dough to baking sheet, spacing them about 1 inch apart. Sprinkle the top of each cookie with granulated sugar.
Bake 15-20 minutes, until the edges of the cookies are light golden brown. Cool cookies completely on a wire rack.
Place cooled cookies on a piece of parchment and drizzle the tops with melted white chocolate. Let the chocolate set at room temperature for about 10 minutes. Store cookies in an airtight container for up to 5 days.