This fruit pizza is really is just an open-faced rustic tart featuring a chewy pizza dough, a creamy mascarpone topping sweetened with brown sugar and flavored with rum, and slices of fresh peaches. The slightly smoky flavor from the hardwood charcoal livens up the fruit wonderfully. If you are using propane, the effect will be subtle, but still luscious and unexpected.
Plan to make the dough several hours before grilling.
Stir together the warm water and sugar, then sprinkle in the yeast and stir. Place in warm area to proof for 5 minutes.
Pour the yeast mixture into a standing mixer's bowl and add 2 ½ cups flour, cornmeal, and salt. Mix on low speed with a dough hook attachment until the dough begins to come together. It should be soft, but smooth and elastic. Add additional flour as needed. Keep mixing until it becomes springy and elastic. The dough should be dry enough to just come way from the walls of the bowl. Then let machine run for 1 minute to further develop the gluten.
Turn the dough out onto a lightly floured board and knead briefly by hand. Coat large mixing bowl with extra oil, place dough in bowl, and turn it over a few times to coat with oil. Cover bowl with plastic wrap and place in warm area, away from drafts to rise. Rise until doubled in bulk, about 1 hour. Punch down, gather into a ball, and let rise again for 40 minutes. Dough is now ready to use, or may be held, well covered with plastic wrap, in refrigerator, for 3 hours. When ready to use, divide into 4 equal balls and place on a rimmed baking sheet pan heavily coated with liquid clarified butter. Cover with plastic wrap.
While dough is rising, make the toppings. Drop the peaches in boiling water for 30 seconds to loosen the peels. Drain, run under cold water, and slip peels off. Cut each peach into very thin 1/8-inch slices. Set aside in a bowl and refrigerate until needed.
Whisk together mascarpone and brown sugar together in a small bowl until smooth. Stir in rum or orange juice, 1 teaspoon at a time, just to taste and until the mixture is very smooth and creamy. Set aside and refrigerate until needed.
Make a fire using hardwood charcoal with the coals all piled on the left side of the grill or fire up half of your gas grill. You need a hot side and a cool side. Have a work table set up next to your grill with your ingredients: your sheet pan with the dough balls, a clean sheet pan heavily coated with liquefied clarified butter (there should be about 1/8-inch of it on the bottom of the pan with extra as needed), bowl of peaches, a set of tongs, mascarpone mixture with 2 teaspoons, and a jar with liquefied clarified butter with a pastry brush. A table on the other side of the grill should have a cutting board, a pizza wheel, and a serving platter.
When the coals have all turned ashen, you are ready to go. Propane grills should be preheated to about 400 degrees.
Take 1 ball of dough and place it on the empty buttered sheet pan. Use your fingers to press it into a very thin flat circle. The size and exact shape of the circle does not matter. Just keep pressing and patting the dough out as thinly as possible. You should be able to see the pan through it.
Quickly lift the pizza with your fingers and transfer directly to the grill to the side over the coals/heat. Cook for however long it takes for the bottom to begin browning and blistering; usually about 3 minutes. Meanwhile, give the top a good coating of clarified butter. When the bottom is browned, flip it over and immediately drag to the cool side of the grill.
Very quickly dot the surface with the mascarpone mixture. Lift peaches with the tongs and scatter peach slices over the pizza. Drag the pizza back over the coals and continue to cook until mascarpone begins to melt and the peaches are heated through.
Immediately drag the pizza over onto the cutting board and hand off to a handy helper to cut into wedges and serve while you begin again with remaining dough balls. It is possible to do 2 or 3 pizzas at a time, all at staggered stages. Serve immediately.