Preheat the oven to 350 °F (175 °C). Grease or line a 9×9-inch baking pan.

In a heat-proof bowl over a pot of simmering water (double-boiler), melt the butter. Remove from heat and whisk in the sugar until smooth. Beat in eggs one at a time, then stir in vanilla.

Whisk together flour, cocoa powder, baking powder, and salt. Gently fold into the butter mixture until just combined.

Pour the batter into the prepared pan and bake for about 25–30 minutes, until a toothpick inserted in the center comes out with a few moist crumbs. Don’t overbake—brownies should remain fudgy. Allow to cool completely in the pan.

While the brownies cool, prepare the mousse: whip the chilled cream and powdered sugar to soft peaks. Fold in the melted chocolate gently until the mixture is smooth and airy.

Spread the chocolate mousse evenly over the cooled brownies. Chill in the refrigerator for at least 2 hours (or until the mousse is set).

Slice into squares and serve chilled or at cool room temperature.