Instructions

• In a food processor pulse the flour, sugar, lemon zest, and salt until blended. Add the cold butter and pulse again, just until the mixture resembles coarse crumbs. Add ice water, 1 tablespoon at a time, pulsing just until the mixture forms a ball (do not over mix). You may need slightly more or less water. Gather the dough together and form into a thick disk. Wrap in plastic wrap and refrigerate for 1 to 2 hours, until chilled but not hard.
• Preheat the grill for indirect cooking over medium-low heat (300° to 350°F), and preheat a pizza stone for at least 15 minutes, following manufacturer’s instructions.
• In a bowl combine the strawberries, cornstarch, sugar, vanilla, and lemon juice. Let stand for 5 minutes while you roll out the dough.
• Cut a piece of heavy-duty aluminum foil into an 18-inch square and set on an inverted sheet pan. Brush the foil with oil.
• Lightly flour a work surface, a rolling pin, and the dough. Roll the dough into a 12-inch circle. Fold the dough onto the rolling pin and transfer the dough to the foil.
• Put the strawberry mixture and any juices on top of the dough, leaving a 2-inch border. Place the preserves in a microwave-safe dish and warm in a microwave oven on high power until spreadable, 10 to 20 seconds; brush on the strawberries. Top with the almonds. Fold over and pleat the edges of the dough (leaving an opening in the center) and brush the dough with half-and-half. Fold up the edges of the aluminum foil around the crostata to create a 2-inch wall to prevent the juices from spilling over. Gently transfer the foil-stabilized crostata from the sheet pan to the preheated pizza stone. Close the lid and grill over indirect medium-low heat until the strawberries are bubbling and the crust is golden brown, 45 minutes to 1 hour.
  Put the strawberry mixture and any juices on top of the dough, leaving a 2-inch border. Place the preserves in a microwave-safe dish and warm in a microwave oven on high power until spreadable, 10 to 20 seconds; brush on the strawberries. Top with the almonds. Fold over and pleat the edges of the dough (leaving an opening in the center) and brush the dough with half-and-half. Fold up the edges of the aluminum foil around the crostata to create a 2-inch wall to prevent the juices from spilling over. Gently transfer the foil-stabilized crostata from the sheet pan to the preheated pizza stone. Close the lid and grill over medium-low heat until the strawberries are bubbling and the crust is golden brown, 45 minutes to 1 hour.
• Lifting the foil edges, carefully remove the crostata from the pizza stone. Cool for at least 15 minutes before serving. Serve warm or at room temperature.