Combine flour, baking soda and salt in a small bowl; mix well and set aside.
Combine margarine and peanut butter in a mixing bowl; beat on medium speed until blended and smooth. Gradually add both sugars and beat until blended; add egg white and vanilla and beat until smooth. While beating on low speed, gradually add flour mixture and mix until just blended.
Transfer dough to a large piece of plastic wrap and roll into an 8-inch log. Wrap log in plastic wrap and freeze for 2 hours. (Note: You can make the cookie dough up to 3 days in advance and freeze until ready to bake.).
Preheat oven to 350ºF. Coat 2 large baking sheets with cooking spray.
Remove cookie dough from freezer and slice crosswise into about twenty-four 1/3-inch-thick slices; place slices 1 inch apart on prepared baking sheets. Bake until golden around edges, about 8 to 10 minutes. Transfer cookies to wire racks to cool completely. Yields 1 cookie per serving.
Flavor Booster: Browned margarine has a nutty flavor that enhances a peanut butter cookie. Melt the margarine in a small skillet until it sizzles and just begins to brown. Remove from heat and freeze for 20 minutes, or until firm, before using in recipe.