Combine the water, sugar, and yeast in a large bowl and stir until dissolved. Add salt and 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 made 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 15 minutes.
Preheat the oven to 450 degrees F. Place a clean pizza stone in oven to preheat.
Dust a clean work surface lightly with flour. With your fingers and palms, flatten one of the dough rounds into a 10-inch oval about 1/4-inch thick.
In a separate bowl, mix together ricotta, mozzarella, and ham. Spoon 1/4 of mixture just above the center of one oval of dough. Fold the dough to form a half-moon and then press the edges to seal. Fold the edge up with your fingertips and pinch closed to form a ridge all the way around. Repeat with the remaining dough and filling. Place calzones on pizza stone and bake for 15 to 18 minutes, until golden brown. Serve hot.
Recipe courtesy of Mario Batali, 2001