Preheat oven to 175°C (slightly lower for the denser cake). Line 23cm springform pan with baking paper, lightly oil the sides (or use aquafaba to prevent sticking).
Whip aquafaba with electric mixer until soft peaks form (3-4 minutes). Set aside.
If using whole dates, blend soaked dates until smooth. Mix with applesauce, grated ginger, vanilla, and lemon zest.
In large bowl, combine ground hazelnuts, flour, polenta, baking powder, baking soda, cinnamon, and salt.
Fold wet mixture into dry ingredients, then fold in grated carrots. The mixture will be quite thick and dense.
Gently fold in whipped aquafaba in two additions - fold carefully to keep as much air as possible without deflating completely.
Pour into prepared pan. Smooth the top. The batter will be very thick.
Bake 55-65 minutes until toothpick comes out clean and top is deeply golden. The center should feel firm when gently pressed.
Let cool in pan for 15 minutes, then carefully remove springform ring. Cool completely on rack - at least 2 hours.
Wrap in beeswax wrap or container and refrigerate overnight. Swiss carrot cake traditionally improves after a day - it becomes more moist and the flavors meld.