Step 1: In a heavy-bottomed saucepan, combine the granulated sugar and water. Stir gently over medium heat until the sugar is completely dissolved. Once dissolved, stop stirring to prevent crystallization.
Step 2: Increase the heat to medium-high and bring the sugar mixture to a boil. Allow it to cook, without stirring, until it reaches a deep amber color. This usually takes 5-10 minutes. Watch carefully to avoid burning.
Step 3: Immediately remove the pan from the heat. Carefully and slowly pour in the warmed heavy cream while continuously whisking. The mixture will bubble up vigorously. Be very cautious of the hot steam.
Step 4: Add the cubed unsalted butter and white miso paste to the hot caramel. Continue whisking until the butter is fully melted and the miso paste is completely dissolved and incorporated, resulting in a smooth and glossy sauce.
Step 5: Stir in the vanilla extract until well combined.
Step 6: Carefully transfer the miso caramel sauce to a heatproof jar or container. Allow it to cool completely at room temperature. It will thicken considerably as it cools.
Step 7: Store the cooled miso caramel sauce in an airtight container in the refrigerator for up to 2-3 weeks. Reheat gently in the microwave or a saucepan for a pourable consistency.