Preheat oven to 350 degrees F (about 180 degrees C). Grease a round ring mold (9-inch or 23 cm diameter) and dust with flour.
In a blender, blend the carrot, oil and 1 tbsp vanilla together very well until the mixture is homogeneous and smooth. Reserve. In a large bowl, sift the flour and baking powder. Reserve.
Using an electric mixer, beat the eggs and the yolk at medium speed until frothy (about 1 minute). Gradually add the sugar and beat until sugar has been well incorporated (about 1 minute). Stir in the mixture of blended carrots using a spatula.
Then, add the flour/yeast mixture in 3-4 additions and also a pinch of salt, beating on low speed until the flour has been incorporated to the batter (Please, do not overbeat!!!).
Pour batter into the prepared pan. Bake for about 40 minutes or until a toothpick inserted in the center comes out clean. Let cool completely on a wire rack. Unmold and top with chocolate sauce. Decorate as desired.
You can also serve this cake plain or dusted with powdered sugar instead of topping with chocolate sauce. This cake is moist without being oily!!! If you are intolerant to dairy, serve cake dusted with powdered sugar.
To prepare the chocolate sauce: In a saucepan, combine chocolate chips, milk, 1 tbsp vanilla, butter, and honey and cook over medium-high heat, whisking constantly.
When it starts to boil, lower the heat to medium-low and simmer until sauce had thicken (about 5 minutes). Remove from heat, stir in the vanilla extract, and let sauce cool down to warm. Pour over cake.