1. Bring 1 inch of water to a simmer in a medium saucepan over low heat. Place butter in a heatproof bowl set over (but not touching) simmering water and melt butter. Add semisweet and unsweetened chocolates and let stand, stirring often, until melted and smooth. Remove bowl from heat and set aside.

2. Heat milk and 1/3 cup sugar in a medium saucepan over low heat until it begins to steam. Meanwhile, whisk remaining 2/3 cup sugar, cocoa, cornstarch, and salt in a medium heatproof bowl. Add eggs, yolk, and cream; whisk until well combined. Gradually whisk in half of the hot milk mixture. Add cocoa mixture to saucepan with remaining milk mixture and bring to a boil over medium heat, whisking often, making sure to whisk into the corners of the pan. Reduce heat to low and let boil for 30 seconds.

3. Remove from heat. Add melted chocolate mixture, rum, and vanilla; whisk until combined. Pour into six 6-ounce glass jars or individual bowls. Cover with plastic wrap, pressing down on the surface to prevent a skin from forming. Pierce the plastic with the tip of a knife a few times and let cool to room temperature, about 1 hour.

4. Transfer puddings to a refrigerator; refrigerate until chilled, at least 2 hours and up to 3 days. Serve topped with whipped cream and garnished with chocolate shavings.