In a medium saucepan, combine 1 cup of light brown sugar, 1/4 cup of water, and a pinch of salt over medium-low heat. Swirl gently until the mixture begins to boil. Allow it to cook for about 5-6 minutes, or until it turns a deep golden brown. Remove from heat and set aside.

In a separate bowl, whisk together 1 1/4 cups of half and half, 4 egg yolks, and 2 tablespoons of cornstarch until completely smooth.

Gradually pour the cooled caramel into your cream mixture while whisking continuously to temper the eggs and prevent them from curdling.

Pour the combined mixture back into the saucepan and return it to the stove over medium-low heat. Continuously stir for about 5-7 minutes, or until the pudding thickens.

Once thickened, stir in 2 tablespoons of unsalted butter, 2 teaspoons of dark rum (if using), and 1 teaspoon of vanilla extract until fully melted and incorporated.

Allow the budino to cool slightly at room temperature, then top with salted caramel sauce and sprinkle with flaky sea salt. Cover and refrigerate for at least 2 hours before serving.