Preheat oven to 350 degrees. In a small bowl, whisk together the flour and baking soda; set aside. In the bowl of an electric mixer fitted with the paddle attachment, combine the margarine with both sugars; beat on medium speed until light and fluffy. (If you do not have electric mixer, beat well with whisk by hand). Reduce speed to low; add the salt, vanilla, and cornstarch mixture. Beat until well mixed, about 1 minute. Add flour mixture and mix until just combined. Stir in the chocolate chips and peanut butter.
Drop heaping tablespoon-size balls of dough about 2 inches apart on baking sheets lined with parchment paper.
Bake until cookies are golden around the edges and set in the center, 10–12 minutes. Remove from oven, and let cool on baking sheet 1–2 minutes. Transfer to a wire rack, and let cool completely. Enjoy!