Grease the inside of an 8x8 or 9x9 inch nonstick pan (I use baking spray with flour) and line it with parchment paper, leaving an overhang on two sides of the pan.
Prepare the Rosemary Shortbread: In a stand mixer fitted with the paddle attachment, cream the butter, confectioners' sugar and salt on medium-high until light and fluffy, 3-5 minutes. Add the vanilla and rosemary, then lower the speed and gradually add the flour until the dough is smooth.
Press the dough evenly into the prepared pan. Refrigerate for 30 minutes. While the dough is chilling, preheat the oven to 350 degrees F. Once the dough is chilled, bake the shortbread for 25-30 minutes, or until lightly golden on top. Allow shortbread to cool to room temperature.
Prepare the Apricot Filling: In a medium saucepan, combine the apricots, white wine, water, lemon juice, sugar, honey, brandy, and salt over medium heat. Once simmering, cook for 10 minutes, then increase the heat to medium-high. Boil until the remaining liquid is mostly reduced, stirring frequently, about 3-4 minutes. Allow the filling to cool until it's still warm but no longer scorching hot (you can speed this process up in the refrigerator), then transfer to a food processor. Pulse several times to chop the apricots, then puree until smooth but with some texture.
Prepare the Crumb Topping: Place the flour, brown sugar, pecans, and salt in a medium-sized bowl, stirring to combine. Add the butter and then, using a fork or clean fingers, press the ingredients together until the butter is incorporated (some pea-sized pieces of butter here and there are fine).
Spread the apricot filling evenly on top of the shortbread, taking care to make sure it's level (optionally, you can lightly grease the exposed sides of the pan to make sure the filling doesn't stick to the sides). Sprinkle the topping over the apricot layer evenly and gently press into place.
Bake until the topping is golden brown and slightly firm, 25-30 minutes for an 8x8-inch pan, or 20-25 minutes for a 9x9-inch pan. Allow to cool completely before cutting into bars.
Store leftovers in an airtight container at room temperature or in the refrigerator for up to one week. You can also wrap and freeze the bars for up to 3 months (make sure they're not touching or are wrapped individually).