Mix pretzel crumbs, butter, brown sugar and kosher salt in a medium bowl. Reserve 3 tablespoons of the mixture for topping the budinos later. Press 2 tablespoons of the pretzel mixture onto the bottom of an 8-ounce mason jar or ramekin. Repeat with 3 other jars.

Whisk together eggs and cornstarch in a medium bowl, and set aside. Combine brown sugar and water in a medium saucepan, and cook over medium-high heat until a dark caramel forms (7 – 9 minutes). At first, the mixture will produce large bubbles that let out steam. Then the bubbles will get smaller and more rapid. Do not stir during this process. Instead, gently swirl the pan if needed. Eventually, smoke will start rising for the mixture, and you’ll start to smell burnt, toasty aromas. At this point, you’ve got a dark caramel.

Take the mixture off the heat, and immediately whisk in some of the heavy cream and whole milk to stop the cooking. The mixture will bubble up enthusiastically, so don’t add all the liquids at once. If the caramel seizes up (forms a solid mass), just keep on whisking, and it will smooth out. Whisk in the remainder of the heavy cream and whole milk. Return the saucepan over medium-high heat, bring the mixture to a boil, then reduce the heat to medium. Gradually add ladlefuls of the hot caramel to the bowl with the eggs, whisking to combine. Once half the caramel has been incorporated, pour the egg mixture back into the remaining caramel. Cook, whisking constantly, until the mixture is very thick (about 2 minutes). Take the custard off the heat, and whisk in butter and rum. Pour custard through a fine-mesh basket strainer into a clean bowl (preferably with a pour spout). Divide custard between 4 prepared jars. Let cool completely, then cover and refrigerate for at least 4 hours.

Spoon caramel sauce over the surface of each budino. Top with a dollop of whipped cream and sprinkling of pretzel crumbs.