Preheat your oven to 350°F (175°C). This ensures that your cake bakes evenly and achieves the perfect texture.
Grease a 9-inch round cake pan with unsalted butter and dust it with cocoa powder. This will help the cake release easily once baked.
In a double boiler or microwave-safe bowl, combine the finely chopped bittersweet chocolate and unsalted butter. If using a microwave, melt in 30-second intervals, stirring in between until smooth. Once melted, set aside to cool slightly.
Carefully separate the egg yolks from the whites. Place the yolks in one mixing bowl and the whites in another. Be sure no yolk gets into the whites to ensure they whip properly.
Add 1/4 cup of the granulated sugar to the bowl with the egg yolks. Whisk until the mixture is pale and creamy. Gradually incorporate the melted chocolate and butter mixture, mixing until fully combined.
In the bowl with the egg whites, add the cream of tartar and beat until soft peaks form. Gradually add the remaining granulated sugar, continuing to beat until stiff peaks form. This will add volume and lightness to the cake.
Gently fold the whipped egg whites into the chocolate mixture, a third at a time, being careful not to deflate the airy texture. The goal is to create a smooth, homogenous batter.
Pour the batter into the prepared cake pan and smooth the top with a spatula. Bake for 25-30 minutes, or until the center is set but still slightly jiggly. The cake will rise and then fall as it cools.
Remove the cake from the oven and allow it to cool in the pan for about 10 minutes. Then, carefully invert it onto a serving plate and let it cool completely.
Once cooled, dust the top with cocoa powder or powdered sugar for a beautiful finish. Slice and serve this indulgent Baked Chocolate Mousse Cake to your eager guests, and watch their eyes light up with delight.