Preheat the oven to 375°F. Lightly grease a large rimmed baking sheet.

In a measuring cup, whisk together the milk and apple cider vinegar and set aside to curdle.

Combine the flour, sugar, baking powder, salt, and lavender in a large mixing bowl. Add the coconut oil in small clumps, then use your fingers or a pastry cutter to cut it into the flour until the flour texture becomes pebble-like.

Create a well in the center and add the milk mixture and vanilla. Mix with a wooden spoon until about half of the flour is incorporated. Fold in the blackberries and mix until all the ingredients are just moistened, taking care not to overmix.

Place a piece of parchment on the counter. Divide the dough into two blobs. Shape each blob into a disk, roughly 8 inches in diameter. Using a sharp knife, cut one disk in half. Then cut each of those halves into thirds, so that you have 6 cute triangles. Transfer the triangles to a baking sheet, then repeat with the other blob of dough.

Bake until the tops are lightly browned and firm to the touch, 22 to 26 minutes.