Makes 48 cookies
In a medium bowl, sift flour, baking soda and salt. Set aside.
In a large bowl, place the two sugars and butter; combine with a hand mixer. Add vegetable oil, eggs and vanilla; mix to incorporate. Add peanut butter, and mix again. Gradually add dry ingredients into wet, mixing well. The batter may need to be refrigerated to allow it to firm up a bit for easier handling.
With your hands, form the dough into balls and place 2-3 inches (5-7.5 cm) apart on a parchment lined baking sheet. Use a fork dipped in water to make a cross-hatch pattern on top. Sprinkle with Demerara sugar, if desired. Bake at 350°F (180°C) for 24 minutes, or until golden brown. Allow to cool slightly before moving to a cooling rack.