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1
Halve the apricots and remove the pits. Place them into a medium-sized, heavy-bottomed saucepan and place over low heat. No need to add water but just watch the apricots carefully and give them the occasional stir so they don't stick and brown on the bottom of the pan. As the pan heats, they will release their own juices and the fruit will begin to simmer. You can help them along by squashing them a little with a wooden spoon as you do your occasional stir. Simmer for approximately 30 minutes.
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2
At this point, the fruit will be completely soft and fallen apart. Pass it through a very fine sieve over a bowl to remove the skins. Weigh your smooth apricot puree, then place back in the pot over low heat and add the sugar-Artusi calculates that you'll need 800 grams of sugar for every kilo of apricot puree (so 4/5 of the weight of the apricots), which for this amount is usually about 500 grams (17 1/2 ounces).
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3
Heat until the sugar dissolves, stirring often. Continue simmering on low until you reach the consistency desired. If you let this go quite a while, you will get a harder set jam, but even just a short 10 minutes or so will give you a very soft, lovely jam, perfect for this crostata, which has additional cooking time in the oven.
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4
If not using right away, pour the bubbling hot jam into sterilized, dry jars and close the lids. Let them sit on the kitchen bench to cool until you hear that satisfying pop of the lids as they seal.
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5
Combine the flour and sugar in a large bowl or in the bowl of a food process. Cut the cold butter into the flour and sugar by pulsing the processor or, if using hands, rub the butter into the flour until you get a crumbly mixture and there are no more visible butter pieces. Mix in the beaten egg and the yolk along with the lemon zest until the pastry comes together into a smooth, elastic ball. Let it rest in the fridge for at least 30 minutes. Artusi says if you do this the day before, even better.
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6
After the dough has rested, preheat the oven to 350u00b0 F. Divide the dough into two pieces, one slightly larger than the other. Roll this larger one out to about 3-millimeter thickness to cover your pie dish. Roll out the rest of the pastry and with a pastry cutter or sharp knife, cut long strips about 2 centimeters wide. Fill the pie with jam and criss-cross your lattice strips over the top. If you like, use the leftover egg white to brush gently over the top of the pastry. Bake at 350u00b0 F (180u00b0 C) for about 25 minutes, or until the pastry is golden brown and the jam bubbling.
