Last week I upgraded my Windows Github to Github Desktop.
It is certainly a lot faster than that last update they made for Github Windows. It also has a nice little visu
Here's the answer I got from github CS when I contacted them about this:
Thu 2015-08-13 3:38 PM Hi Daniel, Sorry about that! We'll be adding the option to delete branches back in an upcoming release. For now however, here's how you can delete a branch from the Git Shell: Hit ~ in GitHub Desktop to open up the repository in the Git Shell Run 'git branch -d branch_name' When you create a new branch you should see an option to publish it directly in the comparison graph. Let me know if that doesn't make sense or if you have more questions - thanks and sorry for the inconvenience! Robert
I've noticed there is a delay (about 2 or 3 minutes) between deleting the local branch in the shell and git desktop realizing the change.
UPDATE
In 3.0.5 They added Delete the current branch from the gear menu.