To a large heavy bottomed saucepan, add the sugar and flatten out evenly over the entire bottom of the saucepan. Pour the water over the sugar and do not stir.
Heat the sugar and water mixture (without stirring) over medium heat until the sugar is fully dissolved, then increase the heat to medium-high and cook until the mixture turns light amber in color, about 5-10 minutes.
Remove the saucepan from the heat and immediately pour in the heavy cream. The caramel will seize (clump up) and this is normal. Add the butter and stir the caramel until the butter is melted.
Return the saucepan to the stove and heat over medium-low heat, stirring constantly until the clumps have melted and the caramel is smooth.
Remove the caramel from the heat and stir in the vanilla extract. If needed, strain the caramel sauce to remove any small clumps still remaining.
Cool the caramel to room temperature before serving.