Be sure to always use strict; and use warnings; ... for example this line is incorrect:

my %aMenu = { label => "  A", MenuItems => [ @MenuItems ] };
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And should be (warnings would have complained about it):

my %aMenu = ( label => "  A", MenuItems => [ @MenuItems ] );
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As for your root issue, I think you're just looking for another level of hashing ..

# if  @MenuItems actually has something it it, then   MenuItems => [@M
+enuItems]   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;
}
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or, if you don't know the A, B, C menus ahead of time, just make them on the fly as needed:

my %menus;
foreach my $app (map {lc $_} @sorted_applications) {
  $menus{$app} ||= { label => "  ".uc($app), MenuItems => [] };
  push @{ $menus{$app}->{MenuItems} }, $app;
}
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