Combine the wine, yeast and water and stir to dissolve the yeast. Add the honey, salt and olive oil, a turn and a half of the mixing bowl, to the bowl, then stir in a cup of flour at a time to incorporate – stir to combine as much flour as possible, then turn out onto floured pastry board or marble counter and combine by hand, then knead for 6-7 minutes. Rinse the bowl, then dry and lightly oil it, return the dough to the bowl and cover with clean towel. Allow the dough to rise in a warm corner of the kitchen for about 45 minutes.
Cut the dough into four pieces, knead each piece and cover again. Let stand 15 minutes more, or until ready to make the pizzas.
Lightly flour the work surface and roll out each dough to 12-inch discs that are 1/8-inch thick. Top and bake the pizza. Depending on the toppings, the pizzas will cook in 2-4 minutes in a very hot pizza oven.
Alternatively, heat a baking sheet or pizza crust pan or stone in the oven on the hottest setting, 550ºF. Pre-heat for 10-15 minutes. Form the dough, transfer to a cornmeal or flour-dusted rimless baking sheet, then top as you like. Slide the pizzas into the oven or to the hot sheet pan and bake for 5 minutes; switch the broiler on and brown the top, 3-5 minutes more. When you remove the pizza, switch the oven back to the bake setting while you prepare the next pizza. Place the rack one notch higher than the center of the oven for this method.