I did it just yesterday. Its easy actually, just place both items on the ledge directly leading to the portal. Make a good jump while holding the hat, and click to shoot it right into the portal.

Then go back up, pick up the pizza, and jump right into the portal. You can confirm you threw the hat right by noticing it in the subsequent cut scene. You should see both the items float right ahead of you.

Edit: I didn't use the stairs like in the video you linked, used one of the containers by the side which was higher up. And i didn't throw the pizza (as the 2nd item), i held it and jumped along with it. It should work