Learn German: Beim Backen ist mir der Kuchen leider verbrannt. - Unfortunately, my cake burned during baking.

This is the dative of disadvantage. Using the dative pronoun mir instead of a possessive like mein emphasizes that the cake burning was an accident that negatively affected you. It is very similar to saying 'the cake burned on me' in conversational English.

Why does verbrannt take ist as its auxiliary verb here instead of hat?

In this sentence, verbrennen describes an involuntary change of state and does not take a direct object, which means it requires sein. If you were actively burning something on purpose, you would use haben with an accusative object, such as Ich habe das Papier verbrannt (I burned the paper).

Why do we use Beim Backen rather than Während des Backens?

Both phrases mean 'during baking', but beim (a contraction of bei dem) combined with a capitalized verb infinitive is the most natural, everyday way to say 'while doing [action]' in German. Während des Backens requires the genitive case and sounds much more formal or literary.

Could I move leider closer to the beginning of the sentence?