How can I undo git reset --hard HEAD~1?

Pat Notz is correct. You can get the commit back so long as it's been within a few days. git only garbage collects after about a month or so unless you explicitly tell it to remove newer blobs.

$ git init
Initialized empty Git repository in .git/

$ echo "testing reset" > file1
$ git add file1
$ git commit -m 'added file1'
Created initial commit 1a75c1d: added file1
 1 files changed, 1 insertions(+), 0 deletions(-)
 create mode 100644 file1

$ echo "added new file" > file2
$ git add file2
$ git commit -m 'added file2'
Created commit f6e5064: added file2
 1 files changed, 1 insertions(+), 0 deletions(-)
 create mode 100644 file2

$ git reset --hard HEAD^
HEAD is now at 1a75c1d... added file1

$ cat file2
cat: file2: No such file or directory

$ git reflog
1a75c1d... HEAD@{0}: reset --hard HEAD^: updating HEAD
f6e5064... HEAD@{1}: commit: added file2

$ git reset --hard f6e5064
HEAD is now at f6e5064... added file2

$ cat file2
added new file

You can see in the example that the file2 was removed as a result of the hard reset, but was put back in place when I reset via the reflog.

What you want to do is to specify the sha1 of the commit you want to restore to. You can get the sha1 by examining the reflog (git reflog) and then doing

git reset --hard <sha1 of desired commit>

But don't wait too long... after a few weeks git will eventually see that commit as unreferenced and delete all the blobs.

The answer is hidden in the detailed response above, you can simply do:

$> git reset --hard HEAD@{1}

(See the output of git reflog show)