01 - In a small saucepan, combine the chopped pineapple, blackberries, 2 tablespoons granulated sugar, and lemon juice. Cook over medium heat, stirring occasionally, until the fruit softens and breaks down, about 5 to 7 minutes.
02 - Dissolve the cornstarch in 2 teaspoons of water and stir it into the fruit mixture. Continue cooking for 1 minute until thickened. Transfer to a bowl and let cool completely.
03 - In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until evenly combined.
04 - In a large mixing bowl, beat the room-temperature vegan butter and 1 cup granulated sugar using an electric mixer or whisk until light and fluffy.
05 - Add the plant milk and vanilla extract to the butter mixture, mixing until incorporated. Gradually add the dry ingredients, mixing just until a soft dough forms. Do not overmix.
06 - Divide the dough in half. Roll each half between two sheets of parchment paper into a 9x7-inch rectangle about 1/4 inch thick. Spread half of the cooled fruit mixture evenly over each rectangle, leaving a 1/2-inch border on all sides.
07 - Carefully roll up each rectangle from the long side to form a tight log. Wrap the logs in parchment paper and place in the freezer for 20 minutes to firm up.
08 - Preheat the oven to 350°F. Line baking sheets with parchment paper.
09 - Slice each chilled log into 1/2-inch thick rounds. Place the cookies 2 inches apart on the prepared baking sheets.
10 - Bake for 10 to 12 minutes, until the edges are just lightly golden. Allow the cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.