Line a 9-inch square pan with crisscrossed sheets of unbleached parchment paper, each overhanging two opposite sides. Set the pan aside.
In a large bowl, place 2 cups (280 g) of the flour, the xanthan gum, granulated sugar and salt, and whisk to combine well.
Add the butter, and mix to combine. The mixture should come together as a soft dough.
Remove about 3/4 cup (150 g) of the dough and transfer it to a medium-size bowl.
To the reserved dough, add the brown sugar, cinnamon and the remaining 1/4 cup (35 g) flour, and mix to combine. This is the crumble topping.
Place the bowl of crumble topping in the freezer to chill.
Scrape the remaining soft shortbread dough into the prepared square pan, and press into an even layer with well-floured hands.
Set the pan aside.
Slice each of the apricots in half, then remove and discard the pits.
With a serrated knife, carefully slice the apricots into wedges, each about 1/4-inch wide, taking care not to bruise or crush the fruit.
Lay the apricot slices on top of the shortbread in 4 parallel rows, from one side of the pan to the other, overlapping them slightly in each row.
Remove the crumble topping from the freezer, break it up into irregular clumps with a fork, and sprinkle it in an even layer on top of the fruit.
Press down on the topping gently but evenly to help the crumble topping adhere to the fruit.
Place the pan in the center of the preheated oven, and bake for 40 minutes, or until the top is light brown in color and seems set.
Remove the pan from the oven and allow to cool completely.
Carefully remove the bars from the pan by the overhung parchment paper.
With a very sharp knife, slice into 16 equal pieces.
The top half of the bars will be moist and will not set up rock hard because of the moisture in the fruit, but will hold together when handled carefully.