In a large bowl, combine the flour, sugars, salt, baking powder and lemon zest and mix well. Add the butter and work the ingredients together with your fingers until the mixture becomes crumbly, and then use a spatula to mix in the egg and egg yolks until a dough begins to form. Knead the dough a little with your hands, and dust with some flour if it’s too sticky. Place the dough on a flour-dusted clean kitchen counter and roll it into a ball.
Divide the dough into two pieces, one larger than the other (about 60/40 of the total weight). Use your hands to flatten both pieces slightly into a rough circle and wrap separately in plastic wrap. Rest the dough in the fridge for 2 hours. (Make sure you remove the dough from the fridge 30 minutes before you start to work with it so that it’s soft and malleable.)
Lightly dust the base and sides of the greased pie dish with flour, turning over the pan and tapping it to remove any excess.
Use a rolling pin to roll out the larger piece of dough into a circle that’s 10 inches (25 cm) in diameter, and line the pie dish with the edges of the dough loose around the sides of the dish. Place the jam in the center and smooth evenly all the way to the edges, and then fold the sides of the dough 1¼ inches (3 cm) inward over the jam.
Roll the second piece of dough to create a smaller circle, 9 inches (23 cm) in diameter, and place it neatly on top. Use your finger or the back of a fork to neatly tuck the edges of the dough toward the inside of the dish, applying pressure all around the outer perimeter to seal the pieces of dough together.
Leave the cake to chill in the fridge while you preheat the oven to 340°F (170°C). When chilled, remove from the fridge and brush the surface of the cake with the egg wash, then use a fork to score a faint crisscross pattern. Bake for 40 to 45 minutes, or until golden.
Remove the cake from the oven and allow it to cool completely before unmolding. The cake will keep for up to 3 days at room temperature or in the fridge.