Preheat your oven to 350°F. Grease a 9-inch square pan and set it aside.
Make the crumble topping.
Combine all of the topping ingredients (8 tablespoons butter, 1 cup flour and xanthan gum, granulated and brown sugars, and salt), and blend with a fork until well-combined. Place in the refrigerator to chill until ready to use.
Make the cake batter.
Combine the flour, xanthan gum, baking powder, baking soda, salt and granulated sugar in a large bowl, and whisk to combine. Add the light brown sugar and whisk to combine, working out any lumps in the brown sugar.
Add the 2 tablespoons butter, vegetable shortening, and plain yogurt, and mix to combine well.
Add the eggs, one at a time, and the vanilla, beating well after each addition. The batter should be thick, but not stiff. It should spread easily.
Scrape the batter into an even layer in the bottom of the prepared pan.
Make the fruit layer.
In a small bowl, place the blueberries, sugar and salt, and toss to combine. Spread the blueberries out on top of the cake batter in a single, even layer.
Cover the pan securely with aluminum foil, and place it in the center of the preheated oven. Bake for 20 minutes.
Remove the crumble topping from the refrigerator and fluff it with a fork to break it up into irregular pieces.
Remove the pan from the oven, uncover it and sprinkle with the crumble topping in an even layer.
Return the pan to the oven, and bake for another 20 to 25 minutes, until a toothpick inserted into the center comes out with a few moist crumbs attached and the crumb topping is light golden brown.
Remove from the oven, and allow the cake it to cool completely in the pan. Slice into 9 equal squares, and serve.