In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl using a hand mixer), combine oil and both sugars, mixing just until completely combined.
3/4 c vegetable oil, 1/2 c granulated sugar, 1 c packed brown sugar
Add the flax eggs, nondairy milk, vanilla extract, and almond extract. Mix until well combined and smooth, about 1-2 minutes.
Add the flour mixture, mixing until fully incorporated. Scrape the bottom of the bowl to ensure you don't miss any bits of flour.
Using a medium cookie scoop or your hands, scoop dough into 2T-sized balls. Roll in powdered sugar and place on cookie sheet about 1" apart.
1/2 c powdered sugar (for rolling)
Bake for 8-10 minutes, or until tops are nicely cracked and the cracks no longer look wet. Let cool on cookie sheet for 10 minutes, then move to a cooling rack to cool completely.Store in an airtight container for up to 5 days.
Notes
* I use Morton kosher salt. If you use Diamond, you'll want to adjust the amount accordingly.**I used soy milk, but oat, almond, or coconut milk should all work well here.Want to make bigger cookies? Use a large cookie scoop (about 3T), and bake for 12-14 minutes. Makes about 15 cookies.