In a large bowl, mix sliced strawberries with sugar, cornstarch, and lemon juice. Cover and chill until ready to use, then drain any excess juice before filling the crostata.
In a food processor, blend on low speed the sugar, eggs, olive oil, lemon zest and a pinch of salt.
Gradually incorporate ⅔ of the flour and baking powder until the dough begins to form.
Transfer the dough to a work surface and add the remaining flour, whilst working the dough with your hands until you have a smooth even dough (you'll probably have some leftover flour, it's ok). Flatten into a disk, wrap with cling film and store in the fridge for 30 minutes.
Preheat oven to 170°C /340°F (or 150°C/300°F with fan option on), and arrange the oven tray onto the middle shelf.
Cut off a small piece of dough and set it aside for the topping. Roll out the rest on a lightly floured surface until it's about ¼ inch (½ cm) thick. Gently transfer the dough to an 8-inch (20 cm) tart pan, trim any excess around the edges, and prick the base with a fork.
Spread the sliced strawberries over the base to cover it fully and evenly.
Use the reserved dough and any trimmed scraps to make long strips or ropes about 2 cm (⅔ inch) wide. Lay half of the strips over the strawberries, then place the remaining ones on top in the opposite direction to create a simple crisscross pattern.
Bake the jam tart in the oven for 35-40 minutes, or until it's golden on top. Remove from the oven and let it cool completely before cutting into slices.