Whisk buckwheat flour, cornstarch, baking soda, baking powder, and salt in a medium bowl.
In a large bowl mix softened butter, peanut butter, and sugars until creamy. You can use an electric mixer or a hand whisk.
Stir in eggs, and vanilla and mix well. Add the dry ingredients and mix well until you get homogeneous cookie dough. Mix just until well combined.
Cover the dough in plastic wrap and refrigerate for at least 1 hour.
Preheat the oven to 350ºF. Line baking sheets with parchment paper or silicone mats.
Drop large teaspoons of cookie dough on the prepared sheets, spacing them an inch or so.
Use your fingers to gently press down on the balls and flatten them slightly.
Place the chocolate chunks on the surface of the cookies.
Bake for 10 minutes or until golden brown.
Let cool for at least 10 minutes before removing.