Purple Hat and Pizza box console commands for Rare/Rarest Specimen and Pepperoni Precipitation

In steam, add -console to your launch options as shown in the image:

You should also check which key you are using to show the console. I changed mine to comma (,):

You are now ready for entering the console commands. While you are playing, press the button you bound to call the console and it should pop down (and pause the game).

To spawn the Purple Hat write the following:

This will drop the hat in front of you. Now while aiming at the hat, activate the console again and type:

The last step is important, otherwise you will get a generic hat. Similarly for the Pizza Box, for spawning it:
and to name it, while aiming at the box:

Good Luck!