Like this:

-onClick => sub {SUBMIT($blah1, $blah2)}
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That gets me closer, but now that makes my $blah1 variable: Win::32::GUI::Textfield=HASH(01Xc2c35b). I am not sure why this is.

What am I missing?

You are assuming that Button BOK, when calling its own onClick event handler, will pass the text of the Textfield urlfield. This will not work. What *does* get passed is just a copy of the BOK Button object, which you see printing as Win32::GUI::Textfield=HASH(0x1c2c35b). You need to obtain the URL another way.

In the code below, I get the URL by calling the $urlfield->Text() method within the onClick event handler of the BOK Button.
I also made these changes:

• Renamed sub Window_Terminate to sub Main_Terminate, to match the -name you gave your main window.
  A sub named Window_Terminate will never be called in your program, because no object is named Window.
• Added return 1; to the -onClick sub; Always return 1 from a Win32::GUI event handler, unless you *want* to cause alternate behavior, like ignoring the event.
  For a better explanation, see the Win32::GUI::UserGuide::Concepts documentation, updated last month for version 1.02 of Win32::GUI.
• Changed the print to Data::Dumper, because it is a better debugging tool.
• Added -dialogui to Win32::GUI::Window->new(), to enable keyboard navigation.
• Added -tabstop to AddTextfield() and AddButton(), to allow you to tab between them.
• Added -ok to AddButton(), to allow you to press the button by pressing ENTER in the text field.
• Added $urlfield->SetFocus(), so that you don't have to click the Textfield to start typing.
Working, tested code:

use strict;
use warnings;
use Win32::GUI;
use Data::Dumper; $Data::Dumper::Useqq = 1; $| = 1;

my $main = Win32::GUI::Window->new(
  -title     => 'application',
  -name      => 'Main',
  -width     => 400,
  -height    => 200,
  -dialogui  => 1,
);

my $urlfield = $main->AddTextfield(
  -name      => 'urlfield',
  -text      => '',
  -left      =>  10,
  -top       =>  10,
  -width     => 200,
  -height    =>  25,
  -prompt    => ['URL:', 80],
  -tabstop   => 1,
);

$main->AddButton(
  -name      => 'BOK',
  -text      => 'GO!',
  -pos       => [148,125],
  -tabstop   => 1,
  -ok        => 1,
  -onClick   => sub {
# Either of these work:
    my $text = $urlfield->Text();
#   my $text = $main->urlfield->Text();
    SUBMIT( $text );
    return 1;
  },
);

$urlfield->SetFocus();

$main->Show();
Win32::GUI::Dialog();

sub SUBMIT {
  my ($submitted_url) = @_;
  print Dumper $submitted_url;
}

sub Main_Terminate {
  # -1 = Stop message loop and finish program
  return -1;
}
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