About 1 hour before baking, heat the oven to 500°F with a baking steel or stone on the upper-middle rack. In a food processor, combine the parsley, chives, dill, garlic, oil, 1 teaspoon salt and ½ teaspoon pepper.

Process until smooth, about 30 seconds, scraping the bowl as needed. Transfer to a liquid measuring cup and set aside.

Lightly dust a baking peel, inverted baking sheet or rimless cookie sheet with semolina. Transfer one portion of the shaped dough to the peel and, if needed, reshape into a 6-by-12-inch oval.

Sprinkle half the fontina and half the Parmesan evenly over the dough, then layer on half the peperoncini. Slide the dough onto the baking steel and bake until the edges are golden brown, 9 to 11 minutes.

Using the peel, transfer the pizza to a wire rack. Top and bake the second portion of dough in the same way, then transfer to the wire rack. Stir the herb oil to recombine, then drizzle over the warm pizzas.