Gently pat blackberries dry with paper towels, then chop into small pieces about the size of chocolate chips. Spread on a plate and freeze while you prep the dough - this keeps them from bleeding too much into the batter.

Whisk together flour, baking powder, and salt in a medium bowl. Set aside.

Beat softened butter and 1 cup granulated sugar in a large bowl until light and fluffy, about 3 minutes. Scrape down the bowl, then beat in the egg and vanilla until fully combined, about 1 minute more.

Add the flour mixture and beat on low just until no dry streaks remain. The dough will be soft and sticky. Fold in the frozen blackberry pieces with a spatula, working quickly so they don't thaw completely.

Cover the bowl and refrigerate for 15 minutes. This firms up the dough enough to roll. Meanwhile, preheat oven to 350F and line two baking sheets with parchment.

Scoop heaping tablespoonfuls of dough and roll into balls. First roll each ball in granulated sugar for the crackle effect, then roll generously in powdered sugar to coat completely. Place 2 inches apart on prepared sheets.

Bake until tops are crackled and set but centers still look slightly underdone, 10 to 12 minutes. The cookies will look puffed and pale in the cracks, golden at the edges. Let cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.