but i think the second call to MyDB->dbh is independent to the first one and like a new instance of something.

New instance of what? $DBH? no.

{
   package Cow;
   my $i;
   sub moo { print(("moo " x ++$i), "\n"); }
}

Cow->moo();  # moo 
Cow->moo();  # moo moo 
Cow->moo();  # moo moo moo
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{
   package MyDB;
   my $DBH;
   sub dbh {
      if ($DBH) {
         print "found existing $DBH\n";
      } else {
         $DBH = 'dbh';
         print "Init $DBH\n";
      }
   }
}

MyDB->dbh();  # Init dbh
MyDB->dbh();  # Found existing dbh
MyDB->dbh();  # Found existing dbh
[download]