How to form cookie dough into rolls?

A sausage stuffer, perhaps?

Your standard food mill attachment type more typically seen in a home kitchen:

Unless you're seeing some product I've never met, I would not call that stuff "rolled in tubes" - I'd call it a tube (or log) of dough, and I expect the filling process is VERY like a (large, automated) sausage stuffer, and involves no rolling at all.

In making refrigerator cookies, one simply makes a log out of the dough, wraps it, and places it in the fridge to harden before slicing. The dough is not liquid to start with, so it does not pour, and can be shaped without a form. If your "dough" "pours" I'm dubious about your recipe or method.

It really seems to be dependent on the consistency of the dough. Some cookie doughs won't hold shape, as they contain lots of butter and very little flour - chocolate chip cookies are a good example. The upside is that you won't need to shape them into round slices before you bake them, because once in the oven, they'll melt into one big more-or-less round blob regardless of the shape they were in originally (I once tried to make heart-shaped chocolate chip cookies - didn't work). I usually just place a small spoonful or so of dough on the baking rack without flattening it. I also often freeze some dough in an ice cube tray - and when I want cookies, I just throw a few blocks of frozen cookie dough into the preheated oven.

Other cookie doughs, such as sugar cookies, are made to be rolled out and cut using cookie cutters. The dough should contain more flour and should hold its shape well, which means that rolling the dough into a sausage shouldn't be too much work. You could use a cookie press, if you want pretty cookies nearly instantly. If your dough is too soft to handle well, it means that the dough still contains plenty of butter and the butter has become too warm - chilling the dough for a while should help with that, though if you chill it for too long, the butter in the dough may become too hard to handle easily (chilling the dough of sugar cookies is a good idea anyway, it helps them keep their shape).

What kind of cookie dough are you making, and what exactly is so difficult about it?

I don't know about "tools" but I think you're using the wrong paper.

I love parchment paper for some things but this is not an optimal use of it.

You should be using plastic wrap, which is much more similar to the plastic used to hold the tubes of dough. Parchment paper is too rigid to shape the ends of the log without odd creases.

Plastic wrap is strong enough to hold the shape but much more flexible, and it's much easier to work with (if you can keep it from sticking to itself). It's also easy to tie the ends in knots or close them up with twist-ties. Plus, it's more airtight than parchment.

The process I recommend is that you take your dough and pretend it's Play-doh - make it into a tube-shape by hand that is about the diameter you want your cookies - if you want them to be analogous to the Pillsbury ones, aim for about 2 to 2-1/2 inches - and about 10 inches long (make sure it's about 4 inches shorter than your plastic wrap is wide.

Then, take a piece of plastic wrap that is long enough to go all the way around your dough with a decent amount of overlap, put the cookie dough at one edge and roll until the plastic is sealed around it.

Tie up the ends however you like.

When you want to use the dough, open one end and peel it back like a banana, cut your slices, then you should be able to revert the plastic wrap and tie it off at the new cut end.