Place 1/2 cup of the butter, shortening, vanilla, and salt into the bowl of a stand mixer, and beat on high until well combined.
Scrape down the sides of the bowl and then slowly add the powdered sugar on low speed. Once the sugar is mixed in, add the water, continuing to mix on low speed. Once everything is combined, scrape down the sides of the bowl and mix again on medium speed for 2-3 minutes.
Add the remaing 1/4 cup of butter to a small bowl. Mix in the brown sugar, flour, milk, and chocolate chips.
Combine the two mixtures. If the icing is too runny add some extra powdered sugar, and if it is too thick add a little more milk.
Once the cupcakes are cooled completely you can ice them.