# if  @MenuItems actually has something it it, then   MenuItems => [@MenuItems]   is fine
# but for simplicity i just made it MenuItems => []
my %menus = ( a => { label => "  A", MenuItems => [] },
              b => { label => "  B", MenuItems => [] },
              c => { label => "  C", MenuItems => [] },
);
#OR:  my %menus = map { lc($_) => {label => "  $_", MenuItems => []} } 'A' .. 'C';

# then:
foreach my $app (map {lc $_} @sorted_applications) {
  push @{ $menus{$app}->{MenuItems} }, $app;
}