Preheat oven to 325 degrees. Butter a 9-inch springform pan, and set aside.
Make batter: Put butter and chocolate in a heatproof medium bowl set over a pan of simmering water; stir until melted. Let cool slightly.
Whisk together flour, baking powder, and salt in a separate bowl; set aside.
Put sugar and eggs in the bowl of an electric mixer fitted with the whisk attachment, and beat on medium speed until pale and fluffy, about 4 minutes. Add chocolate mixture, milk, and vanilla, and beat until combined. Add flour mixture; beat, scraping down sides of bowl, until well incorporated.
Pour batter into prepared pan. Bake until a cake tester inserted into brownies (avoid center and edges) comes out with a few crumbs but is not wet, 27 to 30 minutes. Let cool completely in pan.
Make topping when brownies are cool: Put chocolate in a medium bowl. Heat cream in a small saucepan over medium-high heat until just simmering. Pour over chocolate; let stand 5 minutes. Gently stir until smooth. Allow ganache to cool, stirring every 10 minutes, until slightly thickened, 25 to 30 minutes.
Pour ganache over cooled brownies in pan; let set, about 20 minutes. Refrigerate until cold, 30 minutes to 1 hour. Let brownies stand at room temperature at least 15 minutes before serving. Lift out brownies; cut into wedges, wiping knife with a hot, damp cloth between each cut. Scatter sprinkles on top.