Pre-heat oven to 350F degrees. Cut the tops off each garlic head. Sprinkle with light oil and salt to taste and wrap loosely in aluminum foil. Place on center oven rack and bake until the garlic is soft and golden, about 45 minutes to an hour.
While the garlic is baking, pour the sugar into a medium saucepan and heat to medium-high. Using a metal spoon, stir the sugar just occasionally, scraping the bottom of the pan. At first the sugar will be lumpy, but will soon melt and start turning brown. Don't stir too often, just enough to keep everything evenly cooking. After about 5 minutes, the sugar should be fully melted and become a rich amber color.
At this point, remove the pan from the heat and immediately add the butter. the mixture will start to bubble quite rapidly. That's just what you want.
Again using a metal spoon, stir the butter and sugar until they melt together almost completely. This takes about a minute.
Next, pour in the heavy whipping cream and sea salt*. The mixture may bubble up and hard at this point, just stir to keep it down.*If you're making regular caramel, add ½ teaspoon of salt and no more. If you're making a salted caramel version, add anywhere from 1 teaspoon to 1½ teaspoons depending on your liking.
Stir constantly now until the sauce is all mixed together and is smooth. Place back on the stove at medium-high heat again for about 20 seconds more. Remember to keep stirring. Remove from heat and set aside.
Once your garlic has finished baking, using your hands, squeeze the softened garlic out of the clove pods. Place the garlic in a small sieve and using the back of a spoon, smash the garlic through the sieve and using the same spoon, scrape the garlic off the under-side of the sieve and whisk into the caramel until fully incorporated. Serve immediately for a hot option or cool 15 minutes to room temperature.
Over several minutes, the caramel will become harder to stir. For a manageable sauce, just heat in microwave for 10-15 seconds and stir again.