Place wine, water and yeast in a large bowl and stir until dissolved. Add the honey, salt and 1 tablespoon olive oil and mix well to combine. Add 1 cup of the flour and mix with a wooden spoon until it becomes a loose batter. Add 2 more cups of the flour and stir for 2 to 3 minutes, incorporating as much flour as you can with the wooden spoon.
Bring the dough together by hand and turn out onto a floured board or marble surface. Knead for 6 to 8 minutes, until dough is smooth and firm. Place in a clean, lightly-oiled bowl, using remaining tablespoon of oil and cover with a towel. Let rise in the warmest part of the kitchen for 45 minutes.
For individual pizzas or calzones, cut the dough into 4 equal pieces and knead into rounds. For one large pizza, knead into 1 large round. For either, let rest for 15 minutes.