01 - Combine granulated sugar and water in a medium heavy-bottomed saucepan. Stir gently, then cook over medium heat without further stirring until the mixture reaches a deep amber color, approximately 6 to 8 minutes.
02 - Remove saucepan from heat and slowly whisk in the heavy cream. The mixture will bubble vigorously; continue whisking until the caramel is smooth.
03 - Add unsalted butter to the caramel and whisk until fully incorporated.
04 - Stir in white miso paste and vanilla extract, if using, until completely dissolved and the sauce achieves a silky texture.
05 - Allow sauce to cool slightly before serving; it will thicken as it cools. Transfer any leftovers to an airtight container and refrigerate for up to two weeks. Rewarm gently before use.