This will sort on the length of the first key found in each inner hash, then ASCIIbetically on the keys of the main HoHoA for ties:

my @sorted = map {substr $_,2}
             sort
             map { pack 'na*', length((%{$HoHoA{$_}})[0]), $_ }
             keys %HoHoA;
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This is a Guttman-Rosler Transform - it packs the length of the first key of each inner hash (assumption: each inner hash has all keys the same length - you can't guarantee to get an AA.. key rather than a BB.. key as the `first') into 2 bytes in network order (assumption: no inner hash key has length >65535) and appends the main hash key.

The resulting list of strings can be sorted by the fast default sort and the substr throws away the two-byte length marker, leaving just the keys.

HTH

Jonathan