Preheat oven to 375 degrees F. Let piecrusts stand according to package directions. In a large bowl, massage chard for 30 seconds (you should have about 3 cups); set aside.
Unroll piecrusts onto a lightly floured surface. Cut each crust in half. Roll or press each half with your hands until wide enough to trace around an 8-inch plate with a small knife. Discard scraps or reserve for another use. Transfer rounds to a baking sheet.
Layer the chard, goat cheese, dates, and ham in the center of each round. Fold edges over the filling, pleating as necessary and leaving center of filling exposed. Sprinkle with salt and pepper. Bake for 25 to 30 minutes or until golden.