In a broken, interrupted, or fragmented manner; with pauses, gaps, or inability to speak clearly due to emotion.
From 'broken' + -ly adverbial suffix. The adjective 'broken' refers to being fractured or interrupted, and the adverb describes action done in that interrupted way.
'She spoke brokenly through tears' is such a powerful phrase because it literally uses a word about fractures to describe how emotions fragment human speech.
Complete word intelligence in one call. Free tier — 50 lookups/day.