2 1/2 cups double zero flour and 1/2 cup all-purpose flour, sifted together
Combine the wine, water and yeast in a large bowl and stir until the yeast is dissolved. Add the honey, salt and olive oil and mix thoroughly. Add 1 cup of the flour and mix with a wooden spoon to make a loose batter. Add 2 more cups of the flour and stir with the spoon for 2 to 3 minutes to incorporate as much flour as possible.
Bring the dough together by hand and turn out onto a floured board or marble surface. Knead for 6 to 8 minutes, until you have a smooth, firm dough. Place the dough in a lightly oiled bowl and cover with a towel. Set aside to rise in the warmest part of the kitchen for 45 minutes.
Cut the risen dough into 4 equal pieces and knead each portion into a round. Cover again and let rest for 15 minutes.
To make the pizzas: Dust a clean work surface lightly with flour. Working with one piece of dough at a time, use your fingers and palms to flatten the dough into a 10- to 12-inch round, each about 1/8-inch thick.