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No, I had a little look for it. I've seen a couple of people online said that havarti is quite similar. I think you can get it from waitrose, but I haven't tried it myself. I've just been using a block of mozzarella from Costco.
At Tony's Pizza Napoletana in San Francisco, owner and pizza savant Tony Gemignani uses cheddar around the edges. The cheddar comes out reasonably lacy and crisp, but the flavor reminds me more of a crisp-edged grilled cheese. I tried sliced and cubed low-moisture mozzarella and young, soft Jacks. I even gave Havarti a go. In the end, the closest substitute I could find was a 50/50 mix of low-moisture mozzarella (which provides some of that clean, buttery dairy flavor) and Jack (which has plenty of fat and also tanginess).
From a serious eats article, but I am yet to find Jack around us.
I haven't tried it in the Ooni and I don't think it would improve it. The dough is thick enough that it needs about 20/25 minutes in the oven so I'm not sure what it would offer. We have a very basic oven I think it was about £100 from Argos
As a side note I have tried a normal baking tray in the Ooni and it 'pringled'
Tips / advice I have so far
bulk proved for 1.5 hours then pressed roughly into the pan, left for 30 minutes and pressed out again, then left for an hour before topping. I've also been using the magimix to mix the dough, ingredients in for 30 seconds, a couple of coil folds to get into a ball and leave. It's been working well.