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We present a universally-optimal distributed algorithm for the exact weighted min-cut. The algorithm is guaranteed to complete in O(D + √(n)) rounds on every graph, recovering the recent result of Dory, Efron, Mukhopadhyay, and Nanongkai [STOC'21], but runs much faster on structured graphs. Specifically, the algorithm completes in O(D) rounds on (weighted) planar graphs or, more generally, any (weighted) excluded-minor family. We obtain this result by designing an aggregation-based algorithm:arXiv:2205.14967v1 fatcat:zwksvajfojcmfhcg24n7c3ytse