How to change the broken screen?

Your phone is very similar to several other Android phones in that there are two ways to do a screen replacement; with or without the frame. On the version without a frame, you just buy the display consisting of the AMOLED and the digitizer. Replacing it consists of removing enough components to be able to access the screen connector, then separating the old screen from the frame, cleaning it off and gluing a new screen on.

I wasn't able to locate any iFixit-style written guides, but did come across a couple of YouTube videos showing the procedure.

Asus RogPhone Screen Replacement - YouTube

Rog Phone screen replacement sotituzione vetro touch lcd iMaina Assistenza - YouTube

The first one is a little more professionally done, but the second one seems to show some sort of cable connection between the rear case of the phone and the motherboard that doesn't appear in the first video, so that's something you'll have to pay attention to.

Of course you'll need a replacement screen; I usually check places like Amazon, eBay and AliExpress first, but there may well be others as well. Here's one that came up on my admittedly cursory search.

Amazon.com: Screen Replacement for Asus ROG Phone LCD Display Touch Digitizer Frame Panel Full Assembly for Asus ROG Phone ZS600KL 6" AMOLED Black Parts (Not for Phone6) : Cell Phones & Accessories

Check your model number to make sure you get the right screen.

Now the other way to do a screen replacement is to buy the screen already attached to the frame. This type of assembly costs slightly more than the screen alone, but in my experience the priced difference is never very much; the most I've seen is about $5 USD more for the screen+frame as opposed to just the screen. The advantage here is that you don't have to worry about cleaning off the old frame and correctly gluing the new screen onto the frame. Here's an example of the screen+frame assembly.

Original LCD Screen for Asus ROG Phone ZS600KL Z01QD Digitizer Full Assembly with Frame（Black)

Although replacing the complete assembly is the preferred and recommended method, it requires a completely different procedure since you basically have to gut the phone and move all of the inside components to the new frame. I wasn't able to locate a guide for that particular repair so if you opted to do it that way you'll be blazing a new trail. Hopefully the two guides I mentioned previously would give you enough information to get through the replacement as long as you add in a generous dose of common sense.

Either way, it would be great if you took lots of pictures as you work and use those to make your own iFixit guide so people who come after you will have a guide to follow. It's easy, fun and will earn the appreciation of the iFixit community.

Best of luck and let us know how it all turns out!