Thank you for braving this. I really couldn't reconcile a puff pastry pizza concept...dough with extra butter fat plus so much cheese! But their use of multiple cheeses intrigued me so I ended up buying a premade pizza dough (already rolled and docked) from Publix, then spent an inordinate amount of time trying to find Full-fat, low moisture mozzarella. I'm not actually sure that exists? Found the fresh mozzarella easily enough and finally ended up buying Tillamook "Whole Milk" mozzarella snacking treats. Used Rao's pizza sauce and my own pesto. I had used CathyZ's idea of prepping the pesto without the cheese and freezing small portions of that. When ready to use, add the cheese at that point.
However...yeast being yeast, after two days the flat and rolled piece of dough expanded to the point where it was pushing itself out of the container. I pulled off a piece and proceeded to test out the flavors. I liked it, but not enough to do the extra work involved with the crust.
Then...to make absolutely sure, I bought a "fresh roll of thin crust pizza dough" from the refrigerated section. That result was okay but boring. I do think the dough needs to do the work of pulling this all together.
As I suspected (and feared), even though I wasn't totally happy with either of these tests, I ate it all.