Preheat oven to 350°F.
In a large mixing bowl, use a hand mixer on low to combine your oil, butter, and peanut butter.
Add both sugars and cream together with your mixer until well combined (about 45 seconds).
Add the flour, baking soda, and salt and mix until completely combined. It's okay if it's more sandy than smooth.
Beat in vanilla and nondairy milk until smooth.
Use clean hands to form 2 tablespoons of dough into a ball and place on a lined baking sheet. Repeat until all the dough is used up, allowing space for cookies to expand while cooking. You should have enough dough to yield about 15 cookies.
Use a fork to press a crisscross shape into the top of the cookies and flatten the dough just a little bit. This step is what yields that classic crinkle top.
Bake for 15-17 minutes and allow to cool at least 10 minutes before enjoying! Garnish with chopped salted peanuts (optional) for extra salinity and crunch.