Preheat your oven to 350ºF and line your baking sheet with parchment paper.
In a large bowl, mix the sugars and peanut butter until well combined. Add the remaining wet ingredients—non-dairy milk and vanilla extract—and stir until smooth.
Sift in the flour, then add the salt and baking soda. Mix until a soft dough forms. If the dough seems dry or crumbly, slowly add 1-2 tablespoons of plant milk until it's soft and holds together easily.
Use a cookie scoop or about 1 tablespoon of dough for each cookie. Roll the dough into a ball and place it on the baking sheet. Gently press a fork into the top, then press again in the opposite direction to create a criss-cross pattern.
Bake at 350º for 10-12 minutes. The shorter time yields soft cookies. Baking a bit longer gives them crisp, golden edges.
Notes
Use a spoon to scoop the brown sugar into the measuring cup.
Use cold milk to keep the dough firm, so chilling is not required.
The perfect dough will feel soft and smooth, similar to fresh play-dough. It should roll easily and hold its shape without turning sticky.