- With the rack in the middle position, preheat the oven to 450°F (230°C). Line a baking sheet with parchment paper.
- In a bowl, combine the cheeses, green onions and basil. Season with salt and pepper.
- On a floured work surface, cut the dough into six equal pieces. With a rolling pin, roll out one piece of dough at a time into an 8-inch (20 cm) circle. Cover the remaining pieces of dough with a slightly damp dishcloth as you work.
- Place about 1/3 cup (75 ml) of the cheese filling in the centre of one dough circle. Brush half of the border of dough with water. Close the calzone by sticking the dry border to the moistened side, forming an elongated half-moon. Press to seal the edges with your fingers. With a spatula, transfer to the baking sheet. Repeat with the remaining ingredients. Brush the calzones with oil.
- Bake for 15 minutes or until golden. If necessary, finish cooking under the broiler to brown evenly.
Preheat the grill, setting the burners to medium. Oil the grate. Oil the calzones on both sides and place on the grill. Close the lid and cook for 2 minutes on each side or until golden. If necessary, turn off the burners, close the lid and finish cooking with the residual heat.