How can I prevent the cheese on my homemade pizza from hardening too soon? I am on my road to perfecting thin crust pizza, but a major problem is that about 5 to 10 minutes after getting it out of the oven the cheese begins to congeal and harden, making my homemade pizza taste like it just came out of the fridge.

Why does it happen? I know the cheese in commercial pizzas from Dominos or Italian mergheritas from Rome both retain somewhat desirable texture for more than 30 minutes after serving. Even as those pizzas get colder, their cheese "coating" does not harden as mine.

Recipe:
500g white flour /335 ml water with 7g dried yeast and 1tbsp of salt /
knead for 10 minutes or so / proof for 2 hours
/ 220c in the oven for 7 minutes

The cheese was a think layer of grated Parmeggiano Reggiano with 18% Mozarella Fresca and a little olive oil with a sprinkle of kosher salt.
The easiest solution is to use different cheeses.

Most commercial pizzerias, like Domino's or Pizza Hut do not use expensive cheeses like Parmesean or fresh mozzerella... they use crappy cheese designed to be stretchy and to stay that way when warm instead of hot. In general, they use part-skim mozzarella, which is often sold pre-shredded and in hard blocks like you'd find cheddars. This is addressed in another answer, here. 

Hard cheeses like Parmesan are unlikely to melt at all and, when they do, they will firm up quickly as they lose heat. You should rarely expect a hard cheese to melt well. Most of them don't. They also lose a lot of oils when they melt, causing unsightly separation. They're great for a burst of salty cheese flavor but they won't behave like Domino's cheese. This is why it's common to top a completed pizza with shredded Parmesan but you wouldn't want to use it as your primary base cheese for the unbaked pizza.

Fresh cheeses like ricotta and mozzarella have the opposite problem. Their high moisture content will often make pizza unappetizingly soggy.

In contrast, the part skim mozzarella used in pizzerias is specifically chosen because it has low water content.

Check out the two questions linked here for a ton more info.

You should consider doing some research into which cheeses melt well as opposed that separate into an gross mess. Note, this list, like many others includes Asiago but it's important to notice that the list refers specifically to fresh Asiago, not the Parmesan-like aged sibling.