In a large bowl with a mixer cream the butter, shortening, sugar and vanilla at least 5 minutes in order to dissolve the sugar. Do not loose patience.
Stir corn starch in milk and cook until it thickens.
Cool about 10 minutes and then little by little add it to the butter mixture. Beat at low speed until creamy and well blended.
The icing will appear curdled at first, but continue beating it well until it becomes smooth.