Two alternatives to the hash of hashes way come to mind.

Use an anonymous array ref as your object, and store your two hashes inside that:

package XYZ;

use constant {
    HASH1 => 0,
    HASH2 => 1,
}

sub new {
  my $class = shift;
  my $self = [
    { something => 'this' }, 
    { something_else => 'that' }
  ];
  return bless $self, $class;
}

sub method {
  my $self = shift;
  print $self->[ HASH1 ]{ something }, $self->[ HASH2 ]{ something_els
+e };
}
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Use Abigail's Inside-out object technique:

package XYZ;

my( %instances );
sub new {
  my $class = shift;
  my $self = bless \$class, $class;
  $instances{ $self }{ hash1 } = { something => 'this' };
  $instances{ $self }{ hash2 } = { something_else => 'that' };
  return $self;
}

sub method {
  my $self = shift;
  my( $hash1Ref, $hash2Ref ) = @instances{ $self }{ hash1, hash2 };
  print $hashRef1->{ something }, $hashRef2->{ something_else };
}
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