Shell the nuts. Keep 6 to 8 walnut kernels aside.
Finely mix the walnut kernels with half of the sugar in a chopper or blender.
In a salad bowl, whisk the eggs and olive oil until the mixture is homogeneous.
Add the flour, yeast and a pinch of salt. Blend.
Then add the rest of the sugar and the nut + sugar mixture. Mix again.
Pour 2 tablespoons of rum and mix well.
Line a 20/22 cm diameter round cake tin with baking paper and pour in the dough.
Place a few walnut kernels on top of the dough and bake at 180°C for 25 minutes.
For an even more gourmet version, serve with ice cream or custard or a salted butterscotch caramel sauce. You can also make a coffee or chocolate topping.