Preheat the oven to 350°F and grease a small cake pan. Toss the diced apples with the Calvados in a bowl and set aside.
In a mixing bowl, cream the softened butter with 1/2 cup granulated sugar until light. Add the eggs one at a time and mix until combined.
Stir in the flour, baking powder, and 1/4 tsp salt. Fold in the Calvados-soaked apples.
Pour the batter into the prepared pan and bake for 25 to 30 minutes, until a toothpick comes out clean. Let the cake cool in the pan.
While the cake cools, make the caramel. Place 1/2 cup granulated sugar in a saucepan over medium heat and stir until it melts into a golden liquid.
Carefully add the heavy cream and 1/2 tsp sea salt. Stir until smooth, then remove from heat.
Drizzle the warm salted caramel over the cooled cake and scatter the toasted hazelnuts on top before slicing.