First, in a large mixing bowl slowly beat the 1 1/2 cups of butter, flour, granulated sugar, baking soda, salt, vanilla extract, and eggs until well mixed.
Then, remove the dough from the bowl and form into a loose ball. Divide it into 4 sections, cover each in plastic wrap, and refrigerate for at least an hour.
Next, in a mixing bowl, beat 6 tablespoons of butter, confectioners sugar, half and half, vanilla, and a touch of salt. Mix on medium-high until it looks like frosting.