1. Prepare the Apricot Filling:
* In a medium saucepan, combine the chopped dried apricots, water, and sugar.
* Bring the mixture to a simmer over medium heat, stirring occasionally.
* Once simmering, reduce the heat to low, cover, and cook for about 15-20 minutes, or until the apricots are very tender and most of the liquid has been absorbed. Stir occasionally to prevent sticking.
* Remove from heat. Stir in the fresh lemon juice, almond extract (if using), and a pinch of salt.
* Allow the filling to cool slightly. For a smoother filling, you can use an immersion blender to pulse it a few times, or transfer it to a food processor and pulse until it reaches your desired consistency (some prefer it chunky, others smoother). Set aside to cool completely while you prepare the crust.

2. Prepare the Shortbread Dough:
* Preheat your oven to 375°F (190°C). Grease and flour a 9×13 inch baking pan, or line it with parchment paper, leaving an overhang on two sides for easy removal. This is highly recommended.
* In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt.
* Add the cold, cubed butter to the flour mixture. Using a pastry blender, your fingertips, or a food processor, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining. If using a food processor, pulse in short bursts.
* In a small bowl, lightly beat the egg with the vanilla extract.
* Add the egg mixture to the flour and butter crumbs. Mix with a fork or your hands just until the dough starts to come together. Be careful not to overmix; the dough should be crumbly but hold together when pressed.

3. Assemble the Bars:
* Reserve about 1 1/2 to 2 cups of the shortbread dough mixture for the topping.
* Press the remaining dough evenly into the bottom of your prepared 9×13 inch baking pan. Use the bottom of a measuring cup or your fingers to create a firm, even crust.
* Spread the cooled apricot filling evenly over the shortbread crust, leaving a small (about 1/4 inch) border around the edges if possible.

4. Add the Crumble Topping and Bake:
* Crumble the reserved shortbread dough evenly over the apricot filling.
* Bake in the preheated oven at 375°F (190°C) for 30-35 minutes, or until the topping is golden brown and the edges are lightly browned. The filling might be bubbling slightly.

5. Cool and Cut:
* Remove the pan from the oven and place it on a wire rack to cool completely. This is a crucial step! If you try to cut the bars while they are still warm, they will be very crumbly and fall apart. Cooling completely allows the filling to set and the shortbread to firm up. This can take at least 2-3 hours at room temperature, or you can speed it up in the refrigerator after an initial hour of cooling.
* Once completely cooled, if you used parchment paper, lift the bars out of the pan using the overhang. Place on a cutting board.
* Using a sharp knife, cut into squares or bars. For cleaner cuts, you can chill the bars slightly in the refrigerator before cutting, and wipe the knife clean between cuts.