Preheat the oven to 350 degrees
Line baking sheets with parchment paper.
In a small bowl, combine flour, baking soda and salt. In a large bowl, cream together margarine, sugar, brown sugar, applesauce and vanilla.
Add peanut butter and mix well; this may require a hand mixer or some electric beaters at a slow speed. Add dry ingredients to wet ingredients and blend until just mixed.
Drop heaping tablespoon-sized balls of dough onto a baking sheet, about 2 inches apart. These cookies spread very nicely, but you can press them with a fork for that classic peanut butter cookie look.
Bake for 10 minutes, or until tops crack slightly and edges are a little browned. If you are baking more than one sheet at a time, rotate the sheets halfway through the baking time.
Let the cookies cool on the baking sheet for 10 minutes, then transfer them to a cooling rack.
Store cooled cookies in an airtight container at room temperature.
