In a medium saucepan, combine roughly chopped dried apricots, water, and a touch of granulated sugar. Cook over medium heat for 15 to 20 minutes, stirring occasionally, until the apricots are tender and have absorbed the water. Once cooked, remove from heat and stir in fresh lemon juice, allowing the mixture to cool while you prepare the shortbread base.

Preheat your oven to 375°F (190°C) and prepare a 9x13 inch baking pan by either greasing it with butter or lining it with parchment paper.

In a large mixing bowl, whisk together all-purpose flour, granulated sugar, baking powder, and salt. Cut in the cold, unsalted butter until the mixture resembles coarse crumbs.

Mix in the lightly beaten egg and vanilla extract until just combined. Set aside about 1.5 to 2 cups of this dough for crumbling on top later.

Press the remaining dough evenly into the prepared baking pan. Spread the cooled apricot filling over the dough, ensuring even coverage. Crumble the reserved dough on top.

Place the baking pan in the preheated oven and bake for 30 to 35 minutes, until the top is golden brown and the edges are bubbling slightly.

Once baked, remove the pan from the oven and place it on a wire rack to cool completely. Slice into squares or rectangles.