01 - Preheat the oven to 350°F. Line two baking sheets with parchment paper and set aside.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until evenly distributed. Set aside.
03 - In a large bowl, beat the softened vegan butter and granulated sugar with an electric mixer until light and fluffy, about 2 to 3 minutes. Add the unsweetened applesauce, vanilla extract, and plant-based milk. Mix until smooth and fully incorporated.
04 - Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Do not overmix. Divide the dough evenly into two halves.
05 - In a small saucepan, combine the well-drained crushed pineapple, 2 tablespoons granulated sugar, cornstarch, and turmeric if using. Cook over medium heat for 2 to 3 minutes, stirring constantly, until the mixture thickens to a jam-like consistency. Remove from heat, stir in the pineapple extract, and let cool for 5 to 10 minutes.
06 - Knead the cooled pineapple mixture into one half of the divided dough until fully incorporated and evenly colored throughout.
07 - On a lightly floured surface, roll out both the plain vanilla dough and the pineapple dough into equally sized rectangles approximately ¼ inch thick. Place the pineapple dough layer on top of the vanilla dough layer. Starting from the long edge, carefully roll the stacked doughs into a tight log to create the swirl pattern.
08 - Wrap the dough log tightly in plastic wrap and refrigerate for at least 30 minutes, or until firm enough to slice cleanly.
09 - Remove the chilled dough log from the refrigerator. Using a sharp knife, slice into ½-inch thick rounds. Place the slices on the prepared baking sheets, spacing approximately 2 inches apart to allow for spreading.
10 - Bake in the preheated oven for 10 to 12 minutes, or until the edges are just beginning to turn golden. Allow the cookies to cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely.