Translation:A little bit of glögi and one slice of pie, please.
It's one slice OF pie, not one pie, though, hence the partitive (a slice is just one small part of a pie, not the whole pie). "Yksi pala" (one slice) is indeed in the nominative, since it is one whole thing. :)
And so, yes, you use the partitive with numbers other than one (which includes "nolla", zero, as well). "Nolla palaa", "yksi pala", "kaksi palaa", "kolme palaa"... But if you were to continue this in some way, the noun would be in the partitive whatever the case, since zero, one, two etc. slices are all just parts of a bigger thing.
"Yksi kuppi kahvia" - one cup OF coffee
"Yksi lasi maitoa" - one glass OF milk
"Yksi lusikallinen keittoa" - one spoonful OF soup