my $dbh = dbConnect();

sub dbConnect {
  my $dsn = "DBI:mysql:database:localhost";
  my $db_user_name = 'username';
  my $db_password = 'password';

  $dbh = DBI->connect
    ($dsn, $db_user_name, $db_password, {RaiseError => 1}) || 
         die("cannot connect to DB: ".DBI::errstr."\n",$dbh);
  
}

sub foo {
    # Can still see $dbh in here
    my $sth = $dbh->prepare(...);
}