Make the dough:
Place the water in a small bowl, then sprinkle the yeast over the water, then ½ tablespoon of the sugar. Let the yeast foam up for 10 minutes; if it doesn’t, then start again. Transfer the yeast mixture to a medium bowl, then add the rest of the sugar along with the flour, olive oil, and salt. Use a wooden spoon or silicone spatula to stir the ingredients until they come together, then transfer dough to a lightly floured counter and use lightly floured hands to knead, adding a small amount of flour as needed until a loose, slightly shaggy and somewhat sticky dough forms, 1 minute. Clean out the bowl, lightly oil it, out the dough inside and seal with plastic wrap. Let rest in a warm place for 30 minutes until almost doubled in size, then transfer to the refrigerator to continue to rise and proof for another 30 minutes.
Prep the filling:
While the dough is rising, preheat the oven to 500°F. If you don’t have a pizza stone, invert a heavy baking sheet on a rack centered in the oven. Heat the oil and butter in a medium skillet over low heat. Add the garlic and jalapeños and cook, stirring, until softened but not browned, 2-3 minutes. Remove from the heat, transfer to a bowl, let cool for 10 minutes, then stir in the cilantro, scallions, salt, and pepper.
When the dough has risen, generously dust a large piece of parchment with cornmeal and flour and stretch and roll the dough into four 4-inch rounds. Spoon about 1 tablespoon of the garlic-herb filling onto half the oval, stopping at the center and leaving a ¾-inch border around the edges. Sprinkle the Parmesan and mozzarella over the herb filling, then use the parchment to fold the dough over the filling, then gently peel the dough away from the parchment. Press and crimp the dough together so it resembles a flat calzone. Use a small paring knife to slit the top a few times and, if using the pizza stone, slide the parchment-lined onto the pizza stone or inverted baking sheet. Bake until the crust is golden and crisp, 8 to 9 minutes 10 to 14 minutes. Remove it from the oven Serve with marinara!