Position racks in the upper and lower thirds of the oven; preheat to 350°F. Line 2 baking sheets with parchment paper.
Whisk oats, all-purpose flour, whole-wheat flour, cinnamon, baking soda and salt in a medium bowl. Beat tahini and butter in a large bowl with an electric mixer until blended into a paste. Add granulated sugar (or Splenda) and brown sugar; continue beating until well combined-the mixture will still be a little grainy. Beat in egg, then egg white, then vanilla. Stir in the oat mixture with a wooden spoon until just moistened. Stir in chocolate chips and walnuts.
With damp hands, roll 1 tablespoon of the batter into a ball, place it on a prepared baking sheet and flatten it until squat, but don't let the sides crack. Continue with the remaining batter, spacing the flattened balls 2 inches apart.e the cookies until golden brown, about 16 minutes, switching the pans back to front and top to bottom halfway through. Cool on the pans for 2 minutes, then transfer the cookies to a wire rack to cool completely. Let the pans cool for a few minutes before baking another batch.