In a food processor pulse together flour, ⅓ c sugar, baking powder and salt. Add coconut and butter and pulse until there aren’t any butter pieces bigger than a small pea.
Transfer mixture to a bowl, add Chobani and stir to combine. Pat into a ¾-inch circle on a floured surface and divide into 8 wedges.
Use a metal spatula to transfer to a greased baking sheet. Sprinkle with 1 T sugar and bake at 375°F until golden, 22-25 minutes.