Combine all-purpose flour, baking powder, baking soda, salt, sugar, and chopped walnuts in a large bowl. Mix well.
Add butter and knead into a smooth dough. This takes about 5 minutes.
Divide dough into 16 portions. Roll into balls and place on a cookie sheet. Using the back of a spoon, press down onto dough.
Brush top of cookies with egg wash. Bake in 325°F (165°C) oven for approximately 30 minutes.
Remove and cool in pan for 10 minutes. Transfer onto wire rack to cool completely. Store in an air tight container.