Basically a Temporal deck without the topend or heavy influence requirements. Instead it has Hawk and Visage with a side of Chalice. It focuses on "not losing" as opposed to "winning", forcing the opponent to concede out of frustration, deck themselves, or die to birds. The Chalice in the market combined with the Hawks means that you can eventually fill the board up with decent sized units even without Parliament.
Always make sure to keep track of your Hawks and Hawk a Hawk before you run out of Hawks. If you run out of Hawks, you're gonna have a bad time.
In a vacuum Temple Scribe is probably the best target for Hawk (other than Hawk). Fighting through a bunch of Temple Scribes really slows down most decks and having a bunch means Chalice from the market is really nice. But don't be afraid to play it as a chump blocker.
Use Chalice to eventually have a board full of buffed Hawks and a hand full answers forever. Chalice is also good with the other units, but the Hawk synergy is why it's there. As the game goes on the deck transitions to a more unit heavy chalice style control because of all the Hawks, and a lot of the time Marshals, Wasps, and Temple Scribes.
Copperhall Blessing is usually a worse Harsh Rule, but it's really versatile and gets a lot better late in the game, so it's mostly here as a Hawk target. The main drawback is that it usually just costs a card to stall for a turn. But later in the game the engines (Visage, Chalice, Moondial) should be online so buying a turn is a lot more valuable. Plus it's nice to have as a panic button, since it basically makes it so you can't lose for a turn.
Citywide Ban has been really nice. The deck can actually afford to play it as a one-of (my initial concern was that it's too slow), and hitting it with Hawk is pretty good. You can only ban 4 things, so only hit it one time. It's good against other slow decks with, a lot of the time you can win just by banning one or two annoying bombs (like Icaria and Sword of the Sky King against FJS).
Parliament is probably the main real wincon, but it's not needed to win at all so don't be afraid to use the Owls as blockers. But if you can hit it with Hawk that's a good way to win against most decks.
Thanks to Vesaryn on reddit for inspiration and suggestions
Have you tried the straight hooru hawk/Nostrix/press-gang deck? You gain some nice cards with adding time, but this seems overall less powerful for a relatively similar amount of durdle
Final thing, shouldn't moondial be in the market? Edit: i guess chalice is already there, so nvm. It's way stronger
I have played the Nostrix versions of this deck and while they're definitely faster (this is a REALLY slow deck), I don'l know that I'd say they're better or worse. The Hooru version tries to exploit Nostrix's ability by using Hawk to put a lot of copies of something into the deck for the buff. This version tries to exploit Hawk by continually filling the deck with answers until we win by default, meaning we don't have to run real winconditions. Nostrix/Hawk can do the same thing, but Nostrix and Press-Gang aren't good control cards so they dilute the draw and make it harder to stabilize, but they give a good proactive gameplan. This deck doesn't make any compromises like that so it's able to control the game more consistently, but you don't have much of an option to aggressively go for a win.