To make the raspberry sauce, add the raspberries, sugar, water, and lemon juice to a small sauce pan over medium-high heat. Once the mixture comes to a boil, reduce the heat to medium-low and let it simmer for about 10 minutes, or until it has thickened.
Remove the sauce from the heat and strain into a bowl and set aside. Discard the raspberry seeds.
Preheat the oven to 350 F and grease an 8” x 8” baking pan with butter.
For the brownies, mix the eggs, cocoa powder, baking powder, espresso powder, and salt together in a large bowl or in the bowl of your stand mixer until smooth.
In a microwave safe bowl, melt the butter, milk chocolate bars, and sugar together either in the microwave or over a double-boiler on the stove. Heat up until the mixture is hot and shiny, but not bubbling.
Add the butter mixture to the egg mixture and beat until it’s incorporated.
Mix in the flour and walnuts until the walnuts are evenly distributed in the batter.
Pour the batter into the prepared baking pan and spread evenly to the edges of the pan.
Dollop the melted white chocolate and the raspberry sauce over the surface of the batter. Using a toothpick or a knife swirl them into the batter.
Bake for 28-31 minutes until the middle looks just set or until a toothpick in the center comes out clean with a few crumbs on it.
Let the brownies cool completely before cutting into them. Serve at room temperature.