In a heavy saucepan, combine the sugar and water. Swirl to wet all of the sugar, then set over medium-high heat. Brush the sides of the pot with a wet pastry brush to wash down any stray grains of sugar. Do not stir or swirl the pan.

Watch the mixture carefully as it begins to boil and then slowly starts to darken in color. It will take 4 to 8 minutes to achieve the right color, but beware that once the mixture darkens, it can go quickly from perfectly brown to burned, so watch it the whole time. Once the mixture turns a light amber color, reduce the heat to low and swirl gently until the mixture is uniformly deep golden brown.

Remove from the heat and add the cream. The mixture will sizzle and bubble, and the caramel will seize up. Whisk until it is liquid again and thoroughly combined. Place over low heat and whisk in the miso paste until fully incorporated.