Learn German: Die Glasur ist mir zerlaufen, obwohl der Kuchen kalt war. - My icing melted on me, although the cake was cold.

This is the dative of disadvantage. Using mir (to me) instead of a possessive like meine (my) highlights that the icing melting was an involuntary mishap that negatively affected you. It has the exact same feeling as saying 'the icing melted on me' in English.

Why do we use ist instead of hat with zerlaufen?

The verb zerlaufen (to melt or run) describes a change of state, specifically going from solid to liquid. Intransitive verbs (verbs that do not take a direct object) that express a change of state or a change of location always use sein to form the perfect tense.

What is the difference between zerlaufen and schmelzen?

While both mean to melt, zerlaufen specifically describes something losing its shape and spreading out or running. This makes it the most natural verb for icing, butter, or cheese. Schmelzen is a more general term, typically used for ice, snow, or metals.

Just to review, why does the verb war get pushed to the very end of the sentence?

The word obwohl (although) is a subordinating conjunction. It starts a dependent clause, and in German, dependent clauses always send their conjugated verb (in this case, war) to the very end.