Preheat the oven to 350°F (175°C). Take an 8-inch round cake pan, grease it well, and either dust it lightly with flour or line it with parchment paper.

Melt the dark chocolate slowly, either in a double boiler or in short bursts in the microwave. Set it aside for a little while to cool.

In a large mixing bowl, beat the softened butter with the sugar until it’s creamy and light. Add the eggs one by one, making sure each is fully mixed in before adding the next. Stir in the vanilla extract.

Fold in the grated carrots and almond powder, mixing until everything is combined.

In another bowl, sift together the flour, semolina, baking powder, and a pinch of salt. Gradually fold these dry ingredients into the wet mixture. Then, gently mix in the melted dark chocolate until smooth and evenly incorporated.

Pour the batter into the prepared pan, smoothing the top with a spatula. Bake for about 35–40 minutes. Check by inserting a toothpick into the center; it should come out clean. Let the cake rest in the pan for 10 minutes, and then move it to a wire rack to cool completely.

For the frosting: heat the heavy cream in a small saucepan just until it starts to simmer. Pour it over the finely chopped semisweet chocolate and let it sit for 2 minutes. Stir gently until smooth, then mix in the butter. Let it cool a little so it thickens enough to spread.

Once the cake is fully cooled, spread the chocolate frosting evenly on the top and sides. Chill for 15–20 minutes if needed, then slice and serve.