Step 1

Set a large saucepot over medium-low heat. Combine the brown sugar, water, and salt in the pot. Swirl the pot (don’t stir) and heat until boiling. Cook for 5-6 minutes, until a rich brown color is formed. Turn off the heat.

Step 2

While the sugar is cooling, set out a mixing bowl. Mix the half and half, egg yolks, and cornstarch. Whisk well until smooth.

Step 3

Add the dairy mixture to the slightly cooled sugar, whisking continually. The sugar will seize up at first, but will melt down as it cooks.

Step 4

Place the pot back over medium-low heat. Continue to whisk as the mixture becomes smooth and then thickens into firm pudding consistency.

Step 5

Remove from heat. Stir in the butter, rum, and vanilla extract. Then set a fine mesh strainer over a bowl and pour the budino into the strainer. Use a spatula to push it through, if needed.

Step 6

Pour (or scoop) the budino into ½ cup ramekins or serving jars. Allow them to cool slightly, then top with thick caramel sauce and sea salt (if desired.) Cover and refrigerate until ready to serve.