Preheat oven to 350*F. Line a baking sheet with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment or in a mixing bowl using a hand mixer, cream non-dairy butter, sugar, and lemon zest until well combined and fluffy.
8 tablespoon Non-Dairy Butter, 1 Cups Granulated Sugar, 2 teaspoon Lemon Zest
Add the non-dairy milk and vanilla and mix well.
¼ Cup Non-Dairy Milk, 2 teaspoon Vanilla Extract
Add flour, cornstarch, baking soda, and salt, and mix on low until just combined.
1 ¾ Cups All Purpose Flour, ½ teaspoon Baking Soda, ½ teaspoon Kosher Salt, 2 tablespoon Cornstarch
Using a 3-tablespoon cookie scoop, scoop 8 dough balls, evenly spaced, onto a parchment-lined baking sheet. Then, bake in a 350*F oven for 13-16 minutes, or until the edges are set and just starting to brown.
Allow to cool on the baking sheet for 5 minutes before moving to a wire rack to cool completely.
Repeat with remaining cookie dough.