In a large bowl, beat the softened butter with sugar until light and creamy. Add the eggs one at a time, mixing well after each addition. Stir in vanilla extract.
In a separate bowl, combine flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture and mix until a soft dough forms.
Preheat oven to 350°F (180°C).
Line a baking pan (about 9-inch / 22–24 cm) with parchment paper. Press about 2/3 of the dough evenly into the bottom of the pan.
Spread the plum jam evenly over the dough layer.
Take the remaining dough and grate it directly over the jam layer using a coarse grater. No need to chill the dough beforehand — it should be soft but still easy to grate.
Bake for 35–40 minutes, or until the top is golden and slightly crisp.
Let the cake cool completely before slicing. This helps the jam set and makes cleaner cuts.