Use the butter to grease eight 4-ounce ramekins. Sprinkle them with granulated sugar to evenly coat the interior and tap out the excess. Place the ramekins in a baking dish large enough to fit them with at least an inch of space between each ramekin.
In a small saucepan, stir together the sliced rhubarb and ½ cup of the sugar. With the tip of the paring knife, scrape the insides of 1 vanilla bean into the saucepan. Cook over medium heat, stirring often, until the rhubarb is soft, about 15 minutes. Cool completely.
In the bowl of an electric mixer, combine the egg yolks and ¾ cup of the sugar. Beat until very light yellow. Add the vanilla extract and the melted butter, then beat in the milk. In a small bowl, combine the semolina and cake flours, then add them gradually to the egg mixture, beating lightly. Fold in the rhubarb with a rubber spatula. Beat or whip the egg whites with a pinch of salt until foamy. Gradually beat in 2 tablespoons of the sugar and whip until soft peaks form. Gently fold the egg whites in the batter.
Divide the batter among the ramekins. Add enough hot water to the baking dish to come one-third of the way up the side of the ramekins. Cover the entire baking dish with aluminum foil. Bake for 25 to 30 minutes, or until the budini begin to puff slightly. Remove the foil and continue to bake for another 10 to 15 minutes, or until slightly pale golden and set. Remove from the oven and transfer to a rack to cool.
While the budini bake, make the marmellata: In a large saucepan, mix together the rhubarb and sugar. Cook over low heat, stirring the mixture to dissolve the sugar as the rhubarb begins to soften and release its juices. Scrape the insides of the vanilla bean into the pan, add the mint, and continue to stir. Cook the mixture until the rhubarb is tender but still holds its shape, about 10 minutes. Remove from the heat and immediately transfer the marmellata into a shallow dish to facilitate cooking. When completely cool, removed the mint.
Combine the cream and the scraped insides of the remaining vanilla bean in a chilled mixing bowl. Whip on medium speed until soft peaks form. Gradually add the remaining 2 tablespoons of sugar and continue to whip until the cream holds its shape.
Unmold each budino from its ramekin and top with some of the marmellata. Serve with a dollop of vanilla whipped cream.