Pour the granulated sugar and water into a heavy 3-quart saucepan. Gently stir just enough to even out the sugar into a uniform layer.
Place the pan over medium heat and allow the sugar to dissolve. It will first appear cloudy, then gradually turn clear and start bubbling—this usually takes about 3 to 4 minutes.
Avoid stirring once the bubbling begins. Instead, occasionally swirl the pan to keep the caramel moving and brush down the sides with a damp pastry brush if needed to prevent crystallization.
As the mixture continues to cook, the sugar may clump—this is normal. Keep swirling gently and cooking until it transforms into a thickened liquid with a deep amber hue, similar to dark honey. This caramelization phase takes 8 to 12 minutes, so monitor it closely to avoid burning.
Once the desired color is achieved, carefully add the butter. The mixture will foam vigorously—this is expected. Whisk steadily until all the butter has melted and the mixture is smooth.
Remove the pan from the heat and slowly pour in the heavy cream while whisking continuously. The caramel will bubble up again as the cream hits the hot mixture. Continue whisking until fully combined.
Add the vanilla extract and a pinch of salt, whisking until evenly distributed.
Allow the caramel to rest in the pan for 10 minutes to cool slightly. Then pour it into a heatproof, lidded glass jar and let it cool completely. The sauce will continue to thicken as it cools. Store in the refrigerator for up to two weeks. Warm gently before serving if needed.