* Will:

Does anyone know the specific model / submodel of Dual Core 3.4 GHz CPU used
by HP in the DL380 G4?

Yes. There is none. The DL380 G4 uses the old Netburst-based XEON DP
processors (Socket604, 800MHz FSB) which get _very_ hot. So hot that the
only dual core version intel could make was the 2.8GHz XEON. All other
processors are single core only (they do Hyperthreading which emulates
two cores but that's not the same like a dual core processor).

Have a look at the quickspecs:
http://h18004.www1.hp.com/products/quickspecs/12028_div/12028_div.html

There are apparently dual core and single core
versions of the motherboard, and we have the dual core MB. I see in the
maintenance manual these parts:

404715-001: spare for dual core motherboard

Right, this board supports the 2.8GHz Dual Core XEON

379429-001: spare for 3.4 GHz CPU 2MB, but apparently this is a single
core

Exactly.

What I don't see is any valid HP part number for a dual core 3.4GHz CPU.

It should be obvious why you don't see any.

If such a part does not exist, can someone suggest the native model /
submodel of Intel dual core processor that would work in the 404715-001
motherboard, and will it work with the same VRM as what HP supplies for the
3.4 GHz single core CPU?

No, simply because intel never made one.

Benjamin