Peel and finely grate the carrot and sprinkle with lemon juice.
Preheat the oven to 180°C (approximately 350°F). Butter a bundt pan and sprinkle with breadcrumbs. In the bowl of an electric mixer, beat the eggs with the sugar until light and fluffy.
In a bowl, mix together the carrots, soft butter and ground hazelnuts. In a separate bowl, stir together the flour, cornstarch and baking powder and gently fold into the egg mixture. Fold in the carrots mixture and scrape the batter into the bundt pan.
Bake until a wooden pick inserted near the center of the cake comes out clean, about 45 minutes. Remove from the oven and cool the cake in the pan. Run a metal spatula around the edge and center of the cake and invert onto a serving plate.
Before serving, sprinkle with powdered sugar.