In your stand mixer (or by hand if you're hardcore) beat the butter, condensed milk, and vanilla extract together until fully combined.
Remove the mixing bowl from the stand mixer. By hand, add in about a ¼ cup of corn starch at a time, folding together with your spatula. Keep going until the dough is soft, smooth, and shiny, and is just barely moist. You may not use all the corn starch.
Use a cookie scoop or spoon to extract teaspoon sized balls of dough and roll them into smooth balls, spacing them apart on a cookie sheet.
Press a thumb into each dough ball like you're making thumbprint cookies, and finish flattening them with a fork (leaving decorative indentations if you like.)
Chill these cookies in the fridge for 30-60 minutes, minimum. This helps ensure even baking and a thicker cookie.
Preheat your oven to 350℉. Bake the cookies for 12-15 minutes; they'll start to brown on the bottoms and the tops will start to crack.
Remove from the oven and let cool for 20-30 minutes before enjoying. Decorate them, drizzle with icing, dip in chocolate, or whatever you like.