Does Burning Wheel work for you? Whilst not exactly purely about Dwarves; nor with a spelled out, essay format, Dwarf setting, the implied setting for Dwarven characters is pretty neat and works in a lot of details you see of dwarves in most other types of media - Greed, Oaths, Traditionalist societies, etc.
While it is in a sense just "D&D with dwarven PCs" (or at least can be if taken that way) as well as long out of print, the old Basic D&D Gazetteer "The Dwarves of Rockhome" probably still deserves mention -- if only because it remains about the most in-depth look at what a dwarven nation can actually look like that I've personally seen to date. Complete with (of course setting-specific) insights on dwarven culture, politics, psychology, history, and even architecture.
Here is a list of all Dwarven supplements. I don't thinik it is complete but it does have A LOT of material. My personal favoirite is #17 Dwarves by Roll Aid.
The WFRP 2nd ed adventure Karak Azgal deals with a dwarven kingdom but you don't have to play all Dwarves. The 1st ed of WFRP had a 4 splat book campaign called the Doomstones Campaign. That was dealing with all sorts of adventures but you ended up in an abandoned Dwarven Kingdom in the middle of a Dwarven conflict.