Preheat your oven to 350°F (175°C) and line a large baking tray with parchment paper.
In a small bowl, combine the blackberries with 1 tablespoon of sugar and mash them lightly with a fork until they release their juices and form a thick, purple-blue paste.
In a separate large bowl, cream the softened butter and 3/4 cup of sugar together using an electric mixer until the mixture is pale and fluffy, about 3 minutes.
Add the egg and vanilla extract to the butter mixture, beating on medium speed until fully incorporated.
In a medium bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the butter mixture, mixing on low speed until just combined; do not overmix.
Gently fold in the mashed blackberries using a rubber spatula, swirling the fruit through the dough until streaks of blue are visible.
Scoop rounded tablespoons of dough onto the prepared baking tray, spacing them 2 inches apart.
Bake for 12 to 14 minutes, or until the edges are lightly golden and the centers appear set.
Allow the cookies to cool on the tray for 5 minutes before transferring them to a wire rack to cool completely.