For Example, currently my Start Menu looks like the following:
I would like to make the expanded start menu the default without the background "list" since it's empty, like this:
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What you called background "list" is actually the list of applications in your first screenshot, so it is not empty as you said, it's just hidden behind the expanded menu. There is no setting in Windows 10 to make the expanded menu as default, but there is a setting for the list of applications. If you don't want to see it, follow there steps:
Download and install the free Open Source app Classic Shell then configure the Windows menu as you described.