In a medium bowl, whisk together the flours, oats, baking soda and salt; set aside.
In a large bowl, use an electric mixer to combine the peanut butter, brown sugar, butter, honey, egg and vanilla until well blended.
Stir half of the dry mixture into the peanut butter mixture. Then add the second half and stir until all is well-blended. Stir in the chocolate.
Cover the cookie dough with plastic wrap and refrigerate until the dough is more firm and no longer sticky, about 30 minutes.
Preheat the oven to 350°F. Line 2 baking sheets with parchment paper or silpat mats.
With your hands, roll 1 heaping tablespoonful of dough for each cookie into 1 3/4-inch-diameter ball. Arrange the cookie dough balls on the prepared baking sheets, spacing 2 1/2-inches apart. Bake the cookies until puffed, beginning to brown on top and still very soft to touch, about 10 to 12 minutes. Watch closely because they will burn if baked too long. Cool the cookies on the baking sheets for 5 minutes. Using a metal spatula, transfer the cookies to a rack to cool completely.
Notes
*These cookies can be made 2 days ahead of intended serving time. Store in airtight container at room temperature.