In a heavy bottom sauce pot, heat the sugar stirring constantly with a wooden spoon or heat safe spatula over medium heat. It will clump then melt after a few minutes.
Keep stirring. The sugar will dissolve and start turning a light golden amber color. Do not let it get too dark, it will burn and taste bitter.
Add in all of the butter at one time and keep stirring (it will bubble up).
Cook over medium low heat for 2 minutes or just until it is a smooth consistency.
Slowly stream in the cream and keep stirring. The mixture will once again bubble up. Allow to boil for 1 minute.
Remove from heat and stir in spiced rum and sea salt. Pour into a glass jar.
Allow to cool at room temperature before storing in the refrigerator.
It can be kept out for gifting but should be refrigerated after that. Warm slightly before serving.