A company with no history called Stonemore is selling these anti-package-theft mailboxes.

Boxy and made of powder-coated steel, they're meant to be anchored through the base to a concrete pad. Up top is a letter slot. Below that is a package door, behind which is a hinged floor that drops your package into the compartment below:

The package door also has two metal spring clips, where you can place outgoing letters.

Packages too big to fit through the hinged opening can instead be inserted directly into the compartment below, (if you're willing to give your carrier a key or the code). To retrieve your mail or packages, there's a full-length locked door on the back of the unit.

Shown above is the Hudson model, which runs $430. Below is their less-expensive $300 Cali model, which I think looks better.

Lastly, for those who regularly receive large packages, they offer an Aspen model for $400 that only has a single lid, up top.

The only thing I'm not crazy about is the flat top. Looks cool, sure, but water or snow will just sit up top.