Combine the half and half, milk, rice, and salt in a large saucepan. Bring to a boil, then reduce the heat to simmer. Scrape the seeds from the vanilla bean into the rice mixture, then add the vanilla bean shell. Cover the pot and cook until most of the liquid is absorbed. The rice should look soupy. This should take about 25-30 minutes.Remove the vanilla bean and save for another use.
Transfer the mixture to a bowl. Stir in the sugar and let the mixture cool.
Preheat the oven to 325°F.
Combine the eggs, lemon zest and cinnamon in a small bowl. Stir the mixture into the cooled rice.
Brush six 3 x 1-1/2-inch ramekins with the melted butter. Fill the ramekins 2/3 full with the rice mixture and place them in a baking dish. Pour boiling water along the sides of the baking dish so it comes half way up the sides of the ramekins.
Bake 25-30 minutes or until a knife inserted in the center comes out clean, but the pudding still wiggles when shaken. Remove the ramekins from the baking dish and allow to cool to room temperature before serving, or refrigerate covered until ready to serve.
To make the sauce: Melt the butter in a saucepan over medium heat and stir in the sugar. Cook until the sugar dissolves. Stir in the cherries and continue cooking until the cherries look glazed. Raise the heat to medium high and stir in the amaretto. Cook 1 minute. Transfer the sauce to a small bowl and allow it to cool to room temperature.
To serve the budino: Run a butter knife around the inside edge of each ramekin and unmold each one onto a dessert plate. Spoon some of the cherry sauce over the top; garnish with a mint leaf and serve.