Preheat the oven to 325 F.
If you’re starting with dry tea leaves, put them into a small dish and pour just enough boiling water over them to cover (about a tablespoon or two); set aside for a few minutes, then pour off the water.
In the bowl of a food processor, pulse the butter, sugar and softened tea leaves until well blended and creamy. Add the flour and salt and pulse until the dough comes together.
Roll the dough into walnut-sized balls and place on a parchment-lined sheet. Press down with a cookie stamp, bottom of a glass, or crisscrossed with a fork. (Alternatively, roll the dough into a log, wrap and chill, then slice and bake.) Bake for 10 minutes, or until pale golden around the edges.
Cool on the pan or on a wire rack.