Preheat your oven to 350°F (175°C) and prepare a baking sheet or 9x13-inch baking dish by greasing it lightly.

In a large mixing bowl, cream together softened butter and granulated sugar using an electric mixer on medium speed until light and fluffy.

Add in the egg and vanilla extract and mix on low speed until fully blended.

In a separate bowl, whisk together flour, baking powder, and salt. Gradually add to the wet mixture, mixing just until combined.

In another bowl, stir together rolled oats and brown sugar to create the crumble topping.

Press half of the crumble mixture into the bottom of the greased baking dish, then spread raspberry jam over the base, and sprinkle the remaining crumble mixture on top.

Bake in the preheated oven for 25-30 minutes, checking for a golden brown top.

Let cool in the pan for 10-15 minutes before transferring to a wire rack to cool completely.