Versuchen sie den Nachtisch.
"Nachtisch" = accusative object (masculine).
Versuchen sie unseren Nachtisch.
"unseren Nachtisch" = accusative object
"unseren" is used as an article, a possessive article. It is the accusative masculine form of "unser" because it is the article for "Nachtisch".
Versuchen sie einen Nachtisch.
"einen Nachtisch" = accusative object.
Now "einen" is the article (accusative masculine).
Versuchen sie einen unserer Nachtische.
Now "unserer" is a possessive determiner and not anymore the article! The article job is taken bei "einen"! A possessive determiner is genitive and "unserer" is the genitive masculine plural form of "unser".