Preheat oven to 400 degrees. Spray a baking sheet with nonstick cooking spray.
Heat a large nonstick skillet over medium-high heat. Swirl in the oil, then add the onion, bell peppers, garlic and oregano.
Cook, stirring occasionally, until softened, 5-7 minutes. Stir in the ham and cook 3 minutes.
Remove from heat and let cool slightly.
Turn out the dough onto a lightly floured work surface and divide it in half. Stretch or roll each dough half into a 10-inch circle.
Spread half of the ham mixture over one-half of each circle, leaving a 1-inch border. Top with each with half the cheese.
Fold the dough over, making a half circle, and firmly pinch the edges together to seal (a fork works well).
Using a spatula, transfer the calzones to the baking sheet. Bake until tops are golden brown, about 20 minutes.
Cool 5 minutes, then cut each in half, to make 4 portions.
NOTE: I divide the dough into 4 portions and put 1/4 of the ham mixture and cheese in each, and make a calzone per serving.
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