Line 2 muffin tins with paper liners (you may need a third muffin tin because this batch can make up to 28 cupcakes). Preheat oven to 350º.
In a medium bowl, beat together the cream cheese, 1/3 cup sugar, egg and salt until creamy. Mix in chocolate chips by hand. Set aside.
In a large bowl, whisk together the flour, sugar, cocoa powder, baking soda and salt. Add the water, oil, vinegar and vanilla and beat on medium speed with hand mixer for 2 minutes, scraping sides and bottom of bowl, until combined.
Fill muffin cups 2/3 full with cake batter. Spoon 1 level tablespoon of cream cheese into the center of each cupcake.
Bake for 20-25 minutes. Cool.
Make frosting by beating the butter and cream cheese until smooth. add 2 1/2 cups of powdered sugar and mix until combined. If your frosting is too thin, add up to another 1/2 cup powdered sugar.
Pipe frosting on cooled cupcakes.