Preheat oven to 350°F. Butter and flour a 9-inch springform pan.
Melt chocolate and butter in a large heatproof bowl set over a pan of barely simmering water, stirring until completely smooth. Remove from heat then stir in Aperol, vanilla, and salt. Cool 5 minutes. Whisk together yolks and ⅓ cup sugar until sugar dissolves then whisk into chocolate and cool to room temperature.
Beat whites with a pinch of salt using an electric mixer at medium speed until they just hold soft peaks, then, while continuing to beat, gradually add remaining ⅓ cup plus 1 Tbsp sugar. Beat on medium high until whites are glossy and just hold stiff peaks. Whisk about ⅓ of whites into chocolate, then using a spatula, gently fold in remaining whites just until evenly combined. Pour into pan.
Bake until top just feels dry and starts to crack, about 30 minutes. A toothpick inserted into the center should come out barely sticky but not wet. Cake will fall somewhat as it cools. Let the cake cool in pan to warm or room temperature. Remove ring from pan and dust top generously with confectioners sugar.