Heat the oven to 350°F. Melt 2 tablespoons of the butter in an 8-inch round cake pan placed over low heat on the stovetop. Stir in the brown sugar and 2 tablespoons of the Calvados until the mixture bubbles gently and turns smooth.

Remove the pan from the heat. Arrange the pear slices in a single layer over the caramel. Scatter the chopped walnuts evenly across the pears.

In a mixing bowl, cream the remaining 2 tablespoons of butter with the granulated sugar until light. Beat in the egg, then stir in the remaining 1 tablespoon of Calvados.

Whisk together the flour, baking powder, cinnamon, and nutmeg in a separate bowl. Add half the dry mixture to the butter mixture, followed by the milk, then the rest of the dry mixture. Stir until just combined.

Spoon the batter over the pears and walnuts and spread it evenly. Bake for 30 to 35 minutes, until a toothpick inserted in the center comes out clean.

Let the cake cool in the pan for 10 minutes, then run a knife around the edge and invert it onto a plate. Serve warm or at room temperature.