Split the vanilla beans in half lengthwise and scrape the seeds into a medium pot. You’ll use the leftover 1/2 vanilla bean to make the Braised Pineapple (below).
Place the cinnamon sticks and the empty vanilla beans in an empty tea bag or a square of cheesecloth, then tie with string to create a spice satchet (see Kitchen Note).
Add the milk, empty vanilla beans and cinnamon sticks (or satchet if you’ve made one), as well as the sugar and salt to the vanilla seeds in the pot and heat over medium heat until warm, about 5 minutes. If using vanilla extract instead of beans, add now and stir to combine.
Add the sushi rice and stir to separate the grains. Cook, stirring occasionally and adjusting the heat to maintain a bare simmer, until the pudding thickens and three-fourths of the liquid is absorbed, 45 to 60 minutes.
Add the egg yolk and stir to combine. Transfer the pudding to a bowl and cool to room temperature.
Pour the heavy cream into a chilled bowl and use a hand mixer or whisk to beat until stiff peaks form.
Stir the cooled rice pudding to loosen it. Fold the whipped cream into the pudding until well combined. The texture should be soft and cloud-like rather than stiff.
For each bowl of pudding, add ⅓ cup Candied Pecans to the bottom and line the sides of the bowl with five pieces of Braised Pineapple. Add about ¾ cup rice pudding to the bowls, and serve with a side of the Rum Caramel Sauce.
Heat the oven to 250 degrees. Line a baking sheet with parchment paper.
Whisk the egg white with 1 teaspoon water in a medium bowl until well combined. Add the nuts, sugar, cinnamon and a pinch of salt. Stir to combine and evenly coat the nuts. Pour the nuts onto the prepared sheet and separate as best you can into one layer.
Bake until the nuts are golden brown, about 1 hour, separating the nuts with a wooden spoon halfway through.
While nuts are still warm, break apart any remaining clumps with a fork. Let cool to room temperature on the sheet on a wire rack.
Trim and peel the pineapple then halve it lengthwise and cut out the core. Lay it flat on a cutting board and cut crosswise into 1/4-inch-thick half moons. Reserve 1 tablespoon of any juice on the board to make the Rum Caramel Sauce (below).
Place the cinnamon stick, vanilla bean, cloves and star anise in an empty tea bag or cheesecloth and tie with string to create a spice satchet (see Kitchen Note).
Pour the rum into a large saucepan or straight-sided skillet and add the spice satchet and sugar. Stir to combine. Place the slices of pineapple in the pan in a single layer, trying to space just slightly so as not to overlap them.
Bring the rum to a boil over high heat then reduce the heat to maintain a bare simmer. Cook, shaking the pan occasionally, until the liquid evaporates and caramelizes around the pineapple, about 1 1/2 hours.
Rum Caramel Sauce
Combine the sugar and 2 tablespoons water in a medium heavy-bottomed saucepan and place over high heat, stirring with a wooden spoon to dissolve the sugar. Once the sugar dissolves, stop stirring and continue cooking, swirling the syrup in the pan occasionally, until deep golden brown, about 8 minutes.
Reduce the heat to low and whisk in the butter until smooth (be careful, the syrup will bubble up) then pour in the cream, whisking until smooth.
Add the rum, pineapple juice and a pinch of salt and whisk until combined. Remove the pan from the heat and let the caramel sauce cool to room temperature. The sauce will thicken as it cools.
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