Place wine, water, and yeast in a large bowl and stir until dissolved. Add the honey, salt and 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 and cover with a towel. Let rise in the warmest part of the kitchen for 45 minutes.
Knead the dough into 1 large round and let rest for 15 minutes.
Preheat the oven to 475 degrees F.
Add oregano to tomato sauce and ladle the tomato sauce in an even layer over the dough. Distribute the cheese evenly over the surface of the pizza, press the basil leaves into the sauce and cook in the oven for 10 to 12 minutes, until the crust is golden and the cheese is golden brown.
In a 3 quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.
Recipe copyright 2000, Mario Batali. All Rights Reserved.