In a medium bowl, combine sweet condensed milk, unsalted butter, and vanilla extract. Mix vigorously until smooth and creamy, about 2-3 minutes.

Gradually add cornstarch to the mixture. Start stirring slowly, then knead by hand until the dough is cohesive and not sticky, about 4-5 minutes.

Divide the dough into two equal logs and slice into ¼-inch thick pieces. Roll each piece into a small ball.

Place cookie balls on a parchment-lined baking sheet, flattening each ball slightly. Cover with plastic wrap and refrigerate for 30 minutes.

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

Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.