Let's cook.
Preheat oven to 325°F (160°C). Place four 4-ounce ramekins in a baking dish with high sides.
To make the caramel, combine 1/2 cup granulated sugar and 2 tablespoons water in a small saucepan over medium heat. Cook without stirring until the sugar dissolves and turns a deep amber color, about 5-7 minutes. Immediately pour the hot caramel evenly into the bottom of the prepared ramekins.
In a separate saucepan, gently heat the whole milk and 1/4 cup granulated sugar over medium-low heat until the sugar dissolves and the milk is warm, but not boiling. Remove from heat.
In a medium bowl, whisk together the white miso paste, eggs, and vanilla extract until well combined.
Gradually whisk the warm milk mixture into the egg mixture until smooth. Strain the mixture through a fine-mesh sieve into a clean bowl to remove any lumps.
Carefully pour the strained pudding mixture over the caramel in each ramekin. Pour hot water into the baking dish, reaching about halfway up the sides of the ramekins, to create a water bath.
Bake for 35-40 minutes, or until the edges are set but the center still jiggles slightly. Carefully remove the ramekins from the water bath and let them cool completely on a wire rack.
Once cooled, cover each ramekin with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow the pudding to set fully.
To serve, run a thin knife around the edge of each ramekin, then invert onto a serving plate. The caramel will flow over the pudding.
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