Preheat the oven to 325°F (163°C). Line a baking sheet with parchment paper.
In a large mixing bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy, about 3 minutes.
Add the ube halaya and vanilla extract to the butter and sugar mixture. Mix until fully combined and smooth.
In a separate bowl, whisk together the all-purpose flour, cornstarch, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing gently until a soft dough forms. Do not overmix.
Turn the dough onto a lightly floured surface and gently knead it just until combined.
Roll the dough out to about 1/4 inch thickness.
Use a cookie cutter or knife to cut the dough into desired shapes (approximately 24 cookies).
Place the cookies on the prepared baking sheet, spacing them about 1 inch apart.
Bake in the preheated oven for 18-20 minutes, or until the edges are lightly golden.
Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.