Line the bottom of an 8-inch springform pan with parchment paper.
In a heatproof bowl or double boiler, melt the chocolate. When chocolate is mostly melted, mix in the butter until smooth and remove from heat. Allow to cool slightly for 7-10 minutes.
In two bowls, separate 4 of the eggs. Whisk 2 whole eggs and the 4 egg yolks with ½ cup of the sugar in a large bowl—just until combined. Slowly whisk in the warm chocolate mixture.
In a large bowl, beat the 4 egg whites until foamy, 2 minutes. Gradually add the remaining ¼ cup of sugar into the egg whites, and beat until glossy with soft (not stiff) peaks—5 minutes. Very gently fold about a quarter of the beaten egg whites into the chocolate mixture. Continue folding in the remaining egg whites. Scrape the batter into the pan and smooth the top.
Set the pan on a rimmed baking sheet, and bake until the top is puffed and the center is no longer wobbly—35 to 40 minutes. Be careful not to bake the cake too long.
After the cake is done baking, allow to cool—the center of the cake will sink and form a crater. Let the cake cool completely on a rack before adding whipped cream.
In a medium mixing bowl, whip cream with an electric mixer until soft peaks begin to form. Next add in powdered sugar, vanilla, and peppermint. Beat until whipped cream becomes a bit firmer, 2 minutes–don’t beat too long, as the cream will become very stiff instead of silky.
Remove the cake form by running a knife around the edge. Remove cake from pan and place on platter.
Using a spatula, fill the center of the cake with the whipped cream, gently pushing the cream to the edges of the cake, but do not smooth too much. Sprinkle the top with peppermint candy and serve!