Put butter, sugar and vanilla in a bowl and stir until frothy. Then stir in the eggs. Add the flour mixed with baking powder and the cinnamon. Finely grate the carrots and mix into the batter.
Line the bottom of a springform pan with baking paper, brush the inner edge with butter and dust with flour. Now fill the dough into the mold and smooth the surface. Bake in a preheated oven at 170 ° C for about 40 minutes.