In a medium-sized heavy bottomed saucepan with high sides, whisk the sugar on medium-low until it is melted. The sugar will clump up first but will eventually completely melt. This will take about 10 minutes. Be patient and keep an eye on it to make sure it does not burn, stirring every 30 seconds or so.
Once the sugar has melted, remove from heat immediately and stir in the butter until melted and combined. Be careful in this step because the caramel will bubble rapidly when the butter is added.
Next, pour in the heavy cream, sea salt flakes and vanilla. Stir until everything is combined.
Pour into a small bowl or jar and allow to cool completely before using. Taste a spoonful of cooled caramel. If desired, add more sea salt to taste!
Cover tightly and store for up to 1 month in the refrigerator or 3 months in the freezer. Caramel solidifies in the refrigerator. Reheat in the microwave or on the stove to desired consistency.