Take your butter out of the fridge about 1 hour before baking to allow it to come to room temperature or place it in the microwave for about 10-15 seconds to warm it a little.
Preheat your oven to 375° F (190° C).
With an electric mixer, cream the butter and brown sugar for 1 minute until fluffy. Then add 1 cup of peanut butter, and 1 tablespoon of vanilla extract, and mix for an additional minute. Then add the plant milk and mix for about 30 more seconds.
Turn off the mixer, add the flour, cornstarch, baking soda, and salt, and mix on low until a thick dough is formed.
Add 1/2 cup of vegan chocolate chips and stir well. (At this point you can chill the dough and bake up to 3 days later.)
Use a 1-tablespoon cookie scoop to spoon balls of cookie dough onto an ungreased cookie sheet.
Bake at 375° F (190° C) for 8-10 minutes until they have flattened and are just slightly brown. They will still look pretty soft and doughy, but that's okay, they will firm up when cooled.
Allow cooling for about 5 minutes on the cookie sheet before moving to a flat surface or a cookie rack.
Notes
Your dough should be very firm and hold its shape when spooned onto the cookie sheet.
If you want a firmer crispier cookie, replace the cornstarch with 1 tablespoon of all-purpose flour.