1. In a food processor fitted with the large grating disk, grate the onions; transfer to a bowl. Grate the sweet potatoes and transfer to a second bowl.
2. Divide the oil between 2 large pots and heat over medium-high heat. Divide the onions between the pots and cook, stirring often, until beginning to soften, 8 to 10 minutes. Divide the chard between the pots and cook, stirring, until wilted, 5 to 7 minutes.
3. Divide the vegetable mixture between 2 bowls. Dividing evenly between the bowls, fold in the sweet potatoes, Gruyère, and thyme; season each with 1 ½ teaspoons salt and ½ teaspoon pepper. Spread the sweet potato mixture from both bowls onto a rimmed baking sheet and let cool for 10 minutes.
4. Dividing evenly, spoon the mixture onto one side of each half-circle of piecrust (about ½ cup per piecrust), leaving a ½-inch border. Dot the borders with water, fold the dough over to form a quarter-circle, and press firmly to seal; crimp, if desired. Cut 3 slits in each turnover and brush with the egg.
5. To eat tonight: Bake the turnovers on a parchment-lined baking sheet at 400° F until golden brown, 20 to 25 minutes.
6. To freeze and cook later: Freeze the uncooked turnovers on a parchment-lined baking sheet just until firm, 15 to 20 minutes. Transfer to freezer-safe resealable bags and freeze for up to 3 months. To cook, bake the turnovers from frozen on a parchment-lined baking sheet at 400° F until golden brown, 30 to 35 minutes.
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