Preheat oven to 425°. Coat a large baking sheet with cooking spray.
Scrub potatoes with vegetable brush under cold running water. Peel. Using box grater or shredding blade of food processor, shred potatoes. Turn out on paper towels and press to remove excess moisture.
In a large nonstick skillet over medium heat, heat 2 teaspoons of the oil. Add the onion, sugar and basil. Cook stirring occasionally, until golden, about 12 to 14 minutes. Transfer onions to a large bowl.
Return skillet to heat, add the remaining 3 teaspoons oil and increase heat to medium-high. Add potatoes and ham. Cook, stirring occasionally, until slightly browned, 8 to 10 minutes. Stir into onion mixture in bowl and let cool 5 minutes. Stir in ricotta cheese and mozzarella cheese.
Divide pizza dough in half. On a lightly floured surface, stretch or roll each dough half into a 9-to10 inch circle. Spread half of the potato mixture over one half of each circle. Fold plain dough halves over filling, forming half circles. Pinch edges of dough firmly together to seal. Transfer calzones to prepared baking sheet. Bake 22 to 25 minutes, until golden brown. Cool 5 minutes. Transfer to a cutting board and cut each calzone crosswise into 3 pieces.
Nutritional Analysis per serving: 312 calories, 16 g protein, 45 g carbohydrates, 9 g fat, 2 g saturated fat (25% of calories from fat), 16 mg cholesterol, 2 g fiber, 483 mg sodium.