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.
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Zest a Lemon
Preheat the grill for indirect cooking over medium-low heat (about 150C), 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 46-centimeter 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 30.5-centimeter 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 5-centimeter 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 5-cm 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 5-centimeter 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 5-cm 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.