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.