The quotes are important because of what they do: Without them, the shell catches the pipe before the shell you're invoking (cmd.exe) even sees them.
Without quotes:

{ C:\Windows\System32\cmd.exe /c c:\test\slowproc.cmd } | tee.exe proc
+esslog
[download]

with quotes (hopefully):

C:\Windows\System32\cmd.exe /c { " c:\test\slowproc.cmd | tee.exe proc
+esslog " }
[download]

If you could get rid of the call to tee.exe, you could get rid of using cmd.exe too. Much as I dislike it when a monk rashly suggests the OP turn left after requesting help with turning right, here goes:

Instead of the cmd.exe/tee.exe adventure, have you considered using Perl's fork(), then in the child process: open CMD, "slowproc.cmd|";? You could then write anything you get on <CMD> to STDOUT and a log file. (OK, my Camel is at work, so I'm hoping that I did that right from memory. I will trust the other monks to gently correct if not.)

If you're not interested in going down the fork()'ed path, the other option would be to create a wrapper.cmd that invokes slowproc.cmd with the pipe. Then ask cmd.exe to run wrappers.cmd.

Hope this helps.