Sift the powdered sugar and cocoa powder together. Set aside.
Beat the softened butter and shortening until light and fluffy.
Gradually add about two cups of the sifted powdered sugar/cocoa powder mixture, one 1/2 cup at a time. Stir to combine before adding more.
Add the half-n-half, vanilla, and salt. Stir to combine. Scrape down the sides and bottom of the bowl.
Gradually add the remaining two cups of the sifted powdered sugar/cocoa powder mixture, one 1/2 cup at a time. Stir to combine before adding more. Beat the buttercream until smooth.*
Stir the chocolate buttercream frosting by hand using a wooden spoon or a sturdy spatula to remove any air bubbles.
Store in an airtight container in the fridge or freezer.
Video
Notes
*If the buttercream is too thick/dry, add more half-n-half one tablespoon at a time. Or if it is too wet, add more powdered sugar a little at a time.