When calzones hit the grill, you get charring, crispness, and grill marks that an oven just can’t replicate (and, as an added bonus, you avoid heating up the kitchen). The garlic basting oil, while optional, takes the flavor and appearance to the next level.
To prepare the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a large bowl or the bowl of a stand mixer fitted with a flat beater attachment, combine the flour, water, yeast, olive oil, and salt. Mix until a shaggy, sticky dough forms without any dry, floury patches. This should take less than a minute. Scrape down the sides to gather the dough into a rough ball. Cover and set aside.
After 30 minutes, use a bowl scraper or your wet hand to grab a section of dough from one side, lift it up, and press it down to the middle to seal. Repeat, turning the bowl 90° between each stretch, until the dough won’t elongate easily, about 8 to 12 times total. This process, which is called a bowl fold, replaces kneading.
Cover the bowl and let the dough rest at room temperature, undisturbed, for at least 30 minutes or for up to 3 hours. This forgiving dough will be fine with more or less time, but a longer rise will make shaping easier.
Turn the dough out onto a lightly floured work surface. Gently deflate it and divide it in half (about 270g each).
Round each piece of dough into a rough ball by pulling the edges into the center. Turn the dough seam-side down, cover, and let rest for at least 20 minutes and up to 1 hour, until it’s relaxed enough to stretch and shape.
To make the filling: In a medium skillet or saucepan set over medium heat, cook the olive oil, onion, and red pepper flakes until the onion has softened and begins to color, 3 to 4 minutes. Stir in the spinach and cook until fully wilted, 1 to 2 minutes. Season with salt and pepper and set aside to cool.
To make the basting oil: In a small bowl, whisk together the olive oil and garlic. Set aside.
If using a gas grill, preheat to 350°F, then adjust some burners to medium-low and others to medium-high. If using a charcoal grill, set up two-zone grilling by banking the coals towards one side of the grill, which will create a hot and a less-hot section.
To shape the calzones: Transfer one ball of dough to a semolina- or cornmeal-dusted work surface and sprinkle the top with flour. Use your fingertips to gently press and pull the round into a 9" circle.
Transfer the stretched dough to a semolina- or cornmeal-dusted peel, thin wooden cutting board, or inverted baking sheet. Evenly distribute the cooled fillings on the lower half of the dough, leaving a 1/2" margin at the edge, uncovered. Sprinkle the cheeses over the fillings. Fold the upper half to meet the lower edge, creating a semicircle shape, and press to seal. Crimp the edges together as you would a double-crusted pie, if desired. Repeat with second ball of dough.
To prepare the grill: Use a grill brush to remove any residue and clean the grates. For extra protection against sticking, use tongs to rub a wadded or folded paper towel coated in cooking oil over the grates.
To grill the calzones: Slide the prepared calzones onto the grill, choosing a zone of medium intensity heat. Cook for 8 to 10 minutes, or until the bottom crust is golden brown. Then carefully turn the calzones over, cooking for an additional 10 minutes or until fully baked on both sides. Brush with basting oil in the final minutes of cooking and, if necessary, move calzones to a hotter zone on the grill to add color. (Watch for flare-ups if using the basting oil.) The calzones are done when the crust is firm, golden brown, and charred in spots.
Remove calzones from the grill and brush with additional basting oil. Slice and serve warm with pizza sauce for dipping.
Storage information: Store the cooked calzones in the refrigerator for up to three days. Re-heat in a 350°F oven until warmed through.
Feel free to get creative with the filling — try mushrooms or broccoli rabe in place of the spinach — but keep in mind that all vegetables and meats should be cooked first.
For best results, use the less-hot side of the grill for the majority of the cook time, moving the dough closer to the hotter burners or coals only towards the end, and keep the grill lid closed when possible.
Don’t have access to a grill? To bake the calzones in an oven, place a rack in the center of your oven and preheat the oven to 425°F with a baking steel or stone inside. Transfer the calzones to your preheated steel or stone (here’s how!). Bake for approximately 18 to 20 minutes, until the crust is firm and cooked through. For more color, brush with olive oil (skip the garlic, which is prone to burning), then broil for 2 to 3 minutes, until nicely charred in spots.
