Whisk flour, tea, and salt in a small bowl; set aside.
Put butter, sugar, and orange zest in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy, about 3 minutes. Reduce speed to low; gradually mix in flour mixture until just combined.
Divide dough in half. Transfer each half to a piece of parchment paper; shape into logs. Roll in parchment to 1 1/4 inches in diameter, pressing a ruler along edge of parchment at each turn to narrow the log and force out air. Transfer in parchment to paper towel tubes; freeze until firm, 1 hour.
Preheat oven to 350 degrees. Cut logs into 1/4-inch-thick slices. Space 1 inch apart on baking sheets lined with parchment.
Bake cookies, rotating sheets halfway through, until edges are golden, 13 to 15 minutes. Let cool on sheets on wire racks.
Cookies can be stored in airtight containers at room temperature up to 5 days.
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