In a mixing bowl, beat the butter and sugar just until smooth and creamy. Beat in the vanilla extract.
In a small bowl, mix together the all-purpose flour, rice flour, tea leaves, and salt. Stir the flour mixture into the beaten butter until combined.
Form the dough into a log, about 4-cm in diameter. Wrap with plastic and refrigerate overnight.
When you're ready to bake, preheat your oven at 180 degrees C. Line baking sheets with parchment paper.
Unwrap the dough log and, using a very sharp knife, cut the chilled dough into slices no thicker than ½ cm. Place the slices on prepared baking sheets, spacing them well apart.
Bake the cookies for 8 to10 minutes, rotating the baking sheet midway during baking, until the edges of the cookies are lightly brown. When the cookies are baked, rest them for a few minutes to firm up a bit, then transfer to wire racks. Allow the cookies to cool completely before storing in an airtight container.