In a mixing bowl, blend together the sweet condensed milk, room temperature unsalted butter, and pure vanilla extract using a spatula until well combined, allowing some small lumps of butter to remain.

Gradually add the cornstarch, stirring until the mixture thickens and you can no longer mix with a spatula. Knead with your hands until you have a soft dough.

Divide the dough into two logs and slice them into ¼-inch rounds. Roll each slice into a ball for even baking.

Place the balls on a parchment-lined baking sheet, flatten them with a fork, and chill in the refrigerator for 30 minutes.

Preheat the oven to 350°F (175°C). Bake the cookies for 10-12 minutes or until the bottoms are just golden.

Allow to cool on the baking sheet for 5 minutes before transferring to a cooling rack.