Redirecting stderr to a function

So, I was writing a shell script where I have made a custom log function to be used for custom messages, errors and warning. However, I also wanted to store everything from stderr in this log file, which I thought would be no big deal. I just added the below code.

exec 2> >(Log)

And then I added my Log function to the script

Log() {
    if [ -z "$1" ]; then
        read Message
    else
        Message="$1"
    fi

    ....
}

And it was working great, until I tested it in Born Shell. Here I got an redirect error. So I needed to look around for another way to do this and I stumbled across an article from Chris Siebenmann.  This is a great example, but I needed to append this to the whole script and not just one single command. This however was easy enough, I just needed to append a sub-process to all of my script content.

Log() {
    if [ -z "$1" ]; then
        read Message
    else
        Message="$1"
    fi

    if [ -n "$Message" ]; then
        ....
    fi
}

exec 3>&1

(
    .... Execute everything from here


) 2>&1 >&3 3>&- | Log

Now everything from stderr will be parsed to the function, and it will work with both Bash and Sh.