In a mixer with a paddle attachment, cream the butter. Add the sugar and continue creaming, then add the vanilla and mix. Mix in the flour and salt. Add the milk and chopped chocolate and mix. Roll into 1 1/2-inch balls and dip the top of the ball in chopped peanuts. Place on a cookie sheet 1 1/2 inches apart and push your thumb in the middle to make a depression. Bake until light golden brown, about 10 to 12 minutes. Let cool while you make the filling.
To make the filling, over hot water melt the chocolate then stir in the remaining ingredients. Cool 5 minutes then fill the centers of the cookies. Allow to slightly set, approximately 10 minutes.