Tested on Ubuntu 20.04.3 LTS
Create a shell script in /path/to/my/shellscript/my_shell_script.sh
Add png icon to /home/<USER>/.icons/my-icon.png
Add a file to /home/<USER>/.local/share/applications
named my_shortcut.desktop
File contents:
[Desktop Entry]
Type=Application
Name=MyShellScript
Exec=/path/to/my/shellscript/my_shell_script.sh
Icon=/home/<USER>/.icons/my-icon.png
Categories=Development;
Search in Applications – type „MyShellScript…” > Right-click > Add to favourites.
Done.