Melt the butter in a medium saucepan over medium heat; continue cooking until the butter turns golden brown and smells nutty, about 5 minutes, and then stir in the sugar, cream, water, and salt.
Bring to a simmer, whisking frequently to dissolve the sugar. Temper the egg yolks by slowly drizzling ½ cup of the hot liquid into the egg yolks while whisking continuously.
Whisk the tempered egg yolks into the saucepan and bring up to a simmer; cook 2 minutes, whisking constantly.
Whisk the tapioca slurry into the saucepan and cook until thickened, about 30 seconds, whisking constantly. Turn off the heat and whisk in the vanilla, almond extract, and rum extract (if using).
Transfer the pudding to 6 individual bowls or glasses. Serve the pudding slightly warm or at room temperature topped with whipped cream and ground nutmeg.
Recipe by An Edible Mosaicâ„¢ at https://www.anediblemosaic.com/butterbeer-pudding-inspired-by-harry-potter/