1. Preheat the oven to 375F and center a rack in the middle of the oven. Butter an 8-inch round cake pan. Line the bottom of the pan with a round of wax paper or parchment paper, and butter the paper.

2. Place the butter and the chocolate in a small saucepan and melt over very low heat, stirring constantly. Remove the pan from the heat as soon as the mixture is smooth, transfer to a large mixing bowl, stir in the vanilla and salt, and set aside.

3. Next, make a basil sugar: pulse the sugar and the basil together in a food processor until the basil is very finely chopped and uniformly green in color. The sugar will look slightly wet.

4. Add the basil sugar to the chocolate mixture and whisk until smooth. Whisk in the eggs one at a time, blending completely between additions. Sift the cocoa powder over the batter and fold it in until no dry spots remain. Pour the batter into the prepared pan and smooth out the top with a spatula.

5. Bake the cake for 20 to 25 minutes, or until the top of the cake barely begins to crack. Let cool for about 5 minutes, then invert the cake onto a round serving plate.

6. While the cake cools, make the ganache: place the chocolate and the cream in a small saucepan, and stir constantly over very low heat until melted and smooth. Using a flat spatula or knife, spread the ganache over the top of the cake, letting it drip down the sides, if desired. (Hint: Using the ganache immediately will mean a thin coating that drips easily down the sides of the cake; in this case, it’s best to frost the cake over a cooling rack, then transfer it to a serving plate. You can also let the ganache cool a bit, then spread it just on the top, more like a thin frosting.)

7. Serve warm or at room temperature. To store, let cool completely, then cover and keep at room temperature up to 3 days.