Preheat oven to 375 degrees F. Place oats, half at a time if necessary, in a food processor or blender. Cover and process or blend until oats resemble coarse flour. In a medium bowl, stir together oats, flour, baking powder, and baking soda; set aside. Place tofu in the food processor or blender. Cover and process or blend until smooth; set aside.
In an extra large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add tofu; beat until combined, scraping side of bowl occasionally. Add granulated and brown sugars; beat until combined. Beat in oil and vanilla. Beat in as much of the flour mixture as you can with the mixer. Stir in any remaining flour mixture and the chocolate.
Drop dough by level teaspoons 2 inches apart onto an ungreased cookie sheet. Bake for 8 to 10 minutes or until edges are golden brown. Transfer to a wire rack; let cool.