Preheat oven to 375 degrees F.  Grease or line baking sheets with parchment paper or Silpat liners.  Set aside. 

Using a standing or hand-held mixer, in a large bowl, cream butter and sugar together until fluffy.  Add the eggs and vanilla, beating well.  In a second bowl, sift the flour, baking soda and powder, salt and nutmeg together.  Stir into butter mixture until almost blended.  Stir in oats and walnuts until evenly combined.  Scrape the sides and bottom of the bowl after each addition. 

Using a #20 ice cream scoop or large serving spoon, drop cookies onto baking sheets about 2-inches apart. Press a walnut halve into the top of each dough ball, if desired.  Bake for 13 to 17 minutes, or until golden brown around the edges and on top.  Remove from the oven to cool on wire racks.  Store cookies in a tightly sealed container for up to 1 week, or until eaten up!