Preheat oven to 350 degrees F.
With an electric mixer mix together the butter, oil, and sugars until well blended. Add the eggs and mix well. Blend in the almond extract.
Sift together the flour, baking powder, and salt, add to the wet ingredients and mix until well blended.
Roll cookies into small balls (about the size of a walnut). Press down with a bottom of a glass.
Place cookies in a 350 degree F preheated oven and bake for 13 to 15 minutes or until the bottoms are lightly browned. Place on cooling rack and cool completely.
For the frosting mix together the powder sugar, butter, salt, and almond extract. Gradually add the milk until you have the right consistency. Beat until smooth. Frost cooled cookies.
If desired, before the frosting is dried sprinkle with finely chopped almonds.