01 - Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
02 - In a small bowl, combine ground flaxseed with 2 1/2 tablespoons water. Let rest for 5 minutes until thickened and gelatinous.
03 - In a blender or food processor, puree raspberries with 1 tablespoon sugar until completely smooth. Transfer to a small bowl. Rinse the blender, then puree pineapple chunks with the remaining 1 tablespoon sugar until smooth. Set both purees aside.
04 - In a large mixing bowl, beat softened vegan butter and 1 cup granulated sugar together until light and fluffy. Add the thickened flaxseed mixture, plant-based milk, and vanilla extract. Mix until fully incorporated.
05 - In a separate bowl, whisk together flour, baking soda, baking powder, and salt. Gradually add the dry mixture to the wet ingredients, mixing until a soft, cohesive dough forms.
06 - Split the dough into three equal portions. Gently fold the raspberry puree into one portion and the pineapple puree into the second. Leave the third portion plain.
07 - Pinch off small pieces from each of the three doughs and lightly press them together, swirling without over-mixing to maintain distinct color ribbons. Scoop heaping tablespoons of swirled dough onto the prepared baking sheets, spacing them 2 inches apart.
08 - Bake for 12 to 14 minutes, until edges are set and the tops are just beginning to turn golden. Allow cookies to rest on the baking sheets for 5 minutes before transferring to a wire rack.
09 - Let cookies cool completely on the wire rack before serving. Store leftovers in an airtight container at room temperature for up to 4 days.