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Preheat oven to 350 degrees F. Line a large baking sheet with parchment paper or lightly grease the pan.
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For the bottom layer, use a medium-sized mixing bowl. Combine the flour and salt and then work the cold butter into the flour until you have a crumbly mixture. I used my fingers but you could use a pastry blender or a mixer. Stir in the water and mix until your dough comes together. Your dough will hold together but it will not be smooth.
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Divide your dough in half and put the dough halves on your baking sheet with 4-6 inches of space between them and about 2 inches on each side. Wet your hands and shape each piece of the dough into a log. Then, pat the logs into 10 inch by 3 inch rectangles. Be patient.
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To make the top layer (the choux pastry), boil water, salt and butter in a medium saucepan until the butter is completely melted. Add the flour to the water/butter mixture all at once and stir the mixture until it thickens and begins to steam. Continue stirring until the mixture pulls away from the side of the pan. This will happen very quickly, so watch your pan carefully. Stir a few times past this point and then remove the dough from the stovetop and put your dough into the bowl of an electric mixer. Beat at medium speed for about 30 seconds to one minute to cool it down a bit. Then add the three room-temperature eggs one at a time, beating after each addition. Continue to beat until the eggs are fully incorporated. Mix in the almond extract.
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Divide the batter in half and spread batter on top of the two rectangles of dough you have already positioned on your baking sheet. You can use a spatula or your wet fingers to do this. You will need to be careful that this top layer is spread so that it completely covers the top and sides of the dough rectangles. Do this carefully and smooth the top of the batter when you are through.
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Bake your pastries for 50-65 minutes. They should be a golden brown when they are finished.
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While the pastries are baking, prepare the jam topping. Put your jam into the microwave to warm it and make it more spreadable. I used apricot. The original recipe suggested that the best choices were apricot and raspberry but allowed that any number of jams or preserves could be used.
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When the pastries are fully baked, remove them from the oven and set them on a rack to cool. While they are cooling, spread the warm jam on the top of the pastries and then sprinkle with toasted almonds.
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Allow the pastries to cool completely before drizzling with the icing . To prepare the icing, mix sugar, extract and enough milk or water to make a thick but pourable icing. Add the liquid a bit at a time until your icing is the right consistency. If you get your icing too thin, you can add more powdered sugar. Use a spoon and drizzle this icing in thin lines across the top of your pastry.
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Cut into squares or strips to serve.
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I found that this pastry was exceptional but did not store well, so serve it on the day it is prepared.