Preheat oven. Preheat oven to 350°F (180°C). Line an 8-inch (20 cm) square baking dish with parchment paper.
Prepare miso caramel. Unwrap the caramel candies and place them into a small saucepan on low heat. Once the caramel begins to melt add the miso paste and gradually add in the milk 1 tbsp at a time. Use a whisk to mix and combine the caramel with the miso and milk. Once the sauce starts to slightly bubble at the surface and reaches your desired thickness, remove the saucepan from the heat.
Brown butter. Take a small saucepan and brown the butter on medium heat until all the butter is melted. Turn down to low heat until little brown bits show up on the bottom of the saucepan.
Melt semi-sweet chocolate. Put the semi-sweet chocolate in a medium bowl and pour the browned butter over it. Stir until all the chocolate melts. Set aside.
Mix the wet ingredients. Mix the sugar, room-temperature eggs, vanilla extract and semi-sweet chocolate/browned butter in a stand mixer or by hand using a whisk until combined. Do not over-mix.
Add dry ingredients to wet. Sift the all-purpose flour. Add the all-purpose flour, baking powder and salt to the wet ingredients and use a spatula to gently fold the flour into the mixture.
Pour into baking pan. Pour half the batter into the prepared 8-inch X 8-Inch baking pan. Spread the batter evenly. Pour the miso caramel and spread it evenly over the batter. Pour the remaining brownie batter and spread it over the miso caramel. Smooth the top.
Bake. Bake for 22-25 minutes. Remove from oven and let it cool for 15-20 minutes before removing from the baking pan and cutting them. Enjoy with a glass of milk!