If you can get the dough thin enough, the calzone style has a lot to recommend it. It’s certainly the version that looks most like a waffle. And you don’t have to heat up the oven. The problem with doing it this way is the tendency for it to be too bready. After all, it’s going to have two crusts. If you haven’t, say, been working in a pizzeria for a few years, you might find it difficult to get the dough as thin as it needs to be for this to be optimal.
The alternative, waffling the dough and then topping it and baking it, means the finished product may not completely resemble a waffle. But it’s a more forgiving dough-to-topping ratio. Even if the dough is thicker than you might like, the balance is less likely to be wildly off. Also, if you’re going to make multiple waffled pizzas, this is the way to go. Waffling the dough will take a bit of time, but then you can finish the pizzas in the oven together.
Waffleizer tackles the question “Will it waffle?”
Story related to waffles: A colleague’s brother is a chef, who was objecting to management’s push for him to do a daily special at the restaurant (often it’s whatever’s about to go bad rather than a specialty of the chef). So in protest, he offered up the Awful Falafel Waffle. No more requests to do specials.