Make the dough by creaming butter and powdered sugar in a stand mixer fitted with the paddle until smooth and light, about 2 minutes. Add the egg and mix until fully incorporated. Add flour and ground oats and mix on low just until a soft dough forms. Wrap tightly and refrigerate at least 2 hours or overnight.

Make the filling by creaming butter, powdered sugar, and ground nuts until smooth and fluffy. Add egg yolk and mix to combine. Add cornstarch and mix until fully smooth. Add pistachio paste and mix to a thick, pipeable cream. Transfer to a piping bag and refrigerate if not using immediately.

Roll dough on a lightly floured surface to ⅛-inch/3-mm thickness. Cut into 2½-inch/6-cm rounds. Pipe a small mound of filling in the center of each round. Lightly brush edges with egg white and fold into triangles, pinching firmly at the seams to seal.

Arrange cookies on prepared sheets, spacing evenly. Bake until lightly golden and the filling is set, 15 to 20 minutes. Cool 10 minutes on the sheets, then transfer to a rack to cool completely.

Stir pistachio paste into melted white chocolate. Drizzle over cooled cookies and finish with chopped pistachios. Store in an airtight container at room temperature up to 3 days.