Preheat the oven to 350 degrees F. Line a 8- by 8-inch baking dish with foil, leaving a 2-inch overhang to use as handles to remove the brownies after they have baked.
Add the walnuts to a skillet. Toast until fragrant. Remove from the skillet and roughly chop.
Whisk together the sugar, cocoa and salt in a medium bowl until blended. Add the vanilla to the melted butter and vigorously whisk into the dry ingredients until blended. Whisk in the eggs, one at a time, until completely mixed together. Add the flour and walnuts and stir until just combined. The batter will be thick. Spread the batter into the prepared pan.
Bake until a toothpick inserted into the center comes out clean, about 30 minutes. Remove to a wire rack and let cool for 20 minutes before removing from the pan and slicing into 2-inch squares.
Add the whipping cream to the bowl of a stand mixer and turn the speed to medium. Once it starts to thicken up, add the sugar and vanilla and beat until medium-firm peaks form.