Peel all 4 pears (leaving the stems intact on 3) and place these 3 in a saucepan with water and 1 cup of sugar. Simmer lightly for 20 minutes. Remove the pears from the water and set aside.
Divide the eggs and beat the whites with 1/3 cup of sugar in a large bowl with a handheld mixer until stiff. In a separate bowl, mix the butter, the remaining 1/3 cup sugar, and the egg yolks until smooth. Add the chopped walnuts, flour, cocoa powder, and baking powder. Grate the uncooked pear into the batter. Mix again.
Fold in the beaten egg whites, stir all the ingredients together with a spatula, and pour the batter into a bread pan lined with parchment paper. Add the 3 cooked pears in the center of the form with a bit of distance between the pears. Drizzle 1 tsp caramel sauce around each pear. Bake at 350°F for 35 minutes.
Garnish with a generous layer of powdered sugar and a few halved walnuts. For presentation, slice just in front of the pear stem. Now pause for the oohs and ahhs. Enjoy!