Preheat the oven to 350°F (175°C). Grease a 9×9 inch baking pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy, about 2-3 minutes.
Add the egg and vanilla extract to the butter and sugar mixture. Beat until fully combined.
Gradually add the dry flour mixture to the wet ingredients, mixing until just combined. Do not overmix.
Reserve about 1 cup of the dough for the crumble topping and press the remaining dough evenly into the bottom of the prepared baking pan.
Spread the fruit jam evenly over the pressed dough layer.
Crumble the reserved dough over the jam layer evenly.
Bake in the preheated oven for 28-30 minutes, or until the top is golden brown and the jam is bubbly.
Remove from the oven and allow to cool completely in the pan on a wire rack before cutting into 16 bars.