Prep the pan: Heat oven to 350°F (175°C). Line an 8-inch square pan with parchment, leaving overhang for easy lifting.
Make the miso caramel: In a small saucepan, combine sugar and water.
Cook over medium heat without stirring until the mixture turns deep amber, 6–8 minutes. Swirl the pan if needed. Remove from heat, add butter (it will bubble), then slowly whisk in warm cream until smooth.
Whisk in miso and a pinch of salt. Set aside to cool to a thick-but-pourable consistency.
Mix the wet ingredients: In a bowl, whisk melted butter and brown sugar until glossy. Whisk in the egg, egg yolk, and vanilla until smooth.
Add dry ingredients: Stir in flour, baking powder, and salt just until combined.
Do not overmix. Fold in white chocolate.
Assemble: Spread batter into the pan. Dollop 6–8 spoonfuls of miso caramel over the top.
Use a knife or skewer to gently swirl, keeping distinct ribbons.
Bake: Bake 22–27 minutes, until edges are set and lightly golden, and the center has a slight jiggle. A toothpick should come out with moist crumbs, not wet batter.
Finish and cool: Sprinkle with flaky salt and a few extra white chocolate bits, if using. Cool fully in the pan, then lift out and slice into squares.
Optional drizzle: Warm leftover caramel briefly and drizzle over cut blondies.