Preheat the oven to 350ºF (180ºC). Lightly grease an 8 or 9-inch (20 or 23-cm) square baking dish with butter. Line the dish with parchment paper and set aside.
Place the flour, cocoa, and salt in a bowl and whisk well to combine.
Add the chocolate and butter to a second bowl. Heat together gently, either on half-power in the microwave or using a double-boiler, until the two are melted and can be whisked smooth.
Add the brown and white sugars to the melted chocolate and whisk well to combine. The mixture will look grainy at this point.
Crack one egg into the bowl, whisk vigorously until well mixed, then repeat with the second egg.
Dump the flour mixture into the bowl of chocolate. With a rubber spatula or wooden spoon, gently fold everything together. A few streaks of flour showing in the batter is okay.
Set aside some of the raspberries (about ¼ cup or small handful) to be scattered on top of the brownies. Add the rest of the berries to the bowl, and again, fold everything together gently using a rubber spatula or wooden spoon.
Spoon the brownie batter into the prepared square pan. Using an offset spatula, butter knife, or back of a soup spoon smooth the batter evenly into the pan. Scatter the remaining raspberries across the top of the batter.
Place the pan in the oven and bake the raspberry brownies for 35 to 37 minutes, or until the middle still looks slightly underdone.
Remove the pan from the oven and cool it on a wire rack for at least 20 minutes before using the parchment paper to lift the brownies from the pan. The brownies can be sliced and served while still warm but not hot.
Store cooled brownies in an airtight container on the counter for up to three days or in the fridge for up to one week. The brownies can also be frozen in a large reusable zip-top bag for up to one month.