Consider...

for %addrbook.classify({ .value.substr(0,1).uc }).sort -> $g {
    say "{$g.key}:";
    .say for $g.value».invert».fmt("  %-32s %s");
}

So, the outer loop iterates over the sorted pairs, passing each to $g in the block.

(
  "A" => ["allison\@parrot.org" => "Allison Randal", 
          "audreyt\@audreyt.org" => "Audrey Tang"], 
  "J" => ["jnthn\@jnthn.net" => "Jonathan Worthington",
          "jesse\@fsck.org" => "Jesse Vincent"],
  "L" => ["larry\@wall.org" => "Larry Wall"], 
  "P" => ["pmichaud\@pobox.com" => "Patrick R. Michaud"] 
)