Preheat the oven to 350F at least 10 minutes prior to baking the cookies.
Grease and flour a baking tray or line it with parchment paper.
Mix together the all-purpose flour, baking soda, cornstarch and salt in a bowl. Whisk until well combined and set aside.
Place the softened butter in another bowl. Use a standing mixer or wire whisk to beat it until smooth and creamy.
Bring in both types of sugar: white and brown. Mix again on medium speed until everything becomes fluffy.
Add milk and vanilla extract. Whisk again until well incorporated.
Stir in the dry ingredients mixture, mixing continuously until evenly incorporated.
Fold in the chocolate chips using a spatula.
If the dough seems soft or sticky or both, don’t worry! Place it in the fridge for about half an hour so the butter inside will harden a bit.
If you don’t have time to wait for the dough to sit in the fridge, just scoop it on the tray, leaving enough space between the butter cookies (about 2 inches) because they will spread while cooking. Otherwise you can make small balls of dough (1-inch size) and also make sure to keep a short distance between them. Flatten them a bit with the back of your hand.
Bake for 10-12 minutes. Check for the top to be set and the edges slightly golden. Remove immediately from the oven so you don’t overcook them.
Leave the eggless chocolate chip cookies in the tray for 5 minutes, and then transfer to a wire rack to cool completely. They will set during the cooling process and will reach the desired texture.