Heat the oven to 350 and spread the whole walnuts on a baking sheet. Roast in the oven until slightly fragrant and beginning to brown, about 3 to 5 minutes. Remove walnuts from oven, allow them to cool and then chop them up.
In a mixer, add all of the ingredients except for the butter and chocolate chips and stir just to combine.
Cut in the butter, a tablespoon at a time while the mixer is on medium to medium-high speed. It will take a few minutes of consistent mixing to get everything to combine.
Once all of the butter is incorporated, the dough should appear grainy and not very dough-like.
Using your hands, press all of the dough together and form a cylinder about 8 – 9” long and 2” thick. Wrap tightly with plastic wrap and refrigerate for at least 2 hours (up to 48 hours).
When ready to bake, heat the oven to 325 degrees.
Cut ¼” rounds using a sharp knife.
Space the rounds out on a parchment lined baking sheet. This shortbread does expand while baking, so give the rounds enough space to grow.
Bake for 18 - 20 minutes until edges begin to brown.
Allow cookies to cool a few minutes on the baking sheet before transferring them to a wire rack. Allow cookies to cool completely before fiddling around with them (since they're oat flour, they are a little more sensitive than typical shortbread cookies).
In a saucepan, heat the chocolate chips over medium low. Once the chips begin to melt, stir them consistently until smooth and completely melted. Do not let the chocolate get to a boiling point – medium low should melt the chocolate in about 3 minutes.
Using a spoon, drizzle the melted chocolate over the cookies and if desired, add additional chopped walnuts to the melted chocolate for garnish.