The trick to keeping these chewy, flavorful cookies moist is the low-and-slow baking—45 minutes at 275°F—which allows them to bake through without drying out.
Preheat the oven to 275°F. Line 2 baking sheets with parchment paper.
Place the dates in a medium bowl and cover with hot water. Set aside to soak for 20 minutes. Drain any excess water from the bowl and transfer the dates to a blender or food processor. Add the applesauce and vinegar and blend into a paste. Set aside.
In a large bowl, stir together the rolled oats, oat flour, quick-cooking oats, walnuts, lemon zest, cocoa powder, vanilla powder, baking soda, and salt. Add the date and applesauce paste and use a wooden spoon to mix lightly but well. The mixture should be on the dry side.
Scoop a golf-ball-size portion of dough with your hands. Gently roll it into a ball and then pat it flat; be very gentle and do not compact it. Place the round on the prepared baking sheet and repeat with the remaining dough.
Bake until the tops of the cookies appear crispy and browned, 35 to 45 minutes. Transfer to a wire rack to cool. Store in an airtight container at room temperature for 4 to 5 days (if they last that long without being gobbled up!).