The Great Reforms and Emancipation often overshadow the Crimean War in Russian historiography. Russianists tend to treat the conflict as a prelude to a much greater social and political change, so the war itself gets a little bit lost in the shuffle.

Winfried Baumgart's The Crimean War incorporates a good deal of Russian archival and secondary sources in a very compact history of the war. John Shelton Curtiss's Russia's Crimean War is an older text, but still one that has some valuable insight into Russian events. Curtiss's The Russian Army under Nicholas I, 1825-1855 as well as Frederick Kagan's more recent The Military Reforms of Nicholas I: The Origins of the Modern Russian Army cover the pre-Milyutin army. The relevant chapters on the army and navy in the anthology Russia's Great Reforms edited by Ben Eklof, et al are also a useful adjunct to understanding the legacy of the war on the Russian military establishment. David Moon's article "Russian Peasant Volunteers at the Beginning of the Crimean War," in Slavic Review approaches the war from the angle of the peasantry (and Moon is also one of the go-to names for the Russian peasantry for future reference). Mara Kozelsky's review essay The Crimean War, 1853-56 in Kritika gives a good overview of some of the current historiography produced on the war, including some Russian-language monographs. Finally, Candam Badem's The Ottoman Crimean War has not only a good historiographic overview of the conflict, but also gives the perspective of the Ottomans, which is even more underserved in the anglophone historiography than the Russian perspective.

I hope this helps.