Preheat the oven to 350ºF and place a rack in the upper third of the oven. Grease and flour an 8 inch square baking pan and set aside.
In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
In a medium saucepan, bring 2 inches of water to a boil. In a medium, heatproof bowl, add butter and unsweetened chocolate. Place the bowl over, but not touching, the simmering water and allow to melt, stirring occasionally to incorporate.
Once the butter and chocolate have melted, remove the bowl from the simmering pot and whisk in the brown and granulated sugar.
Whisk in the egg, yolk, and vanilla.
Add the flour mixture all at once and fold into the chocolate mixture with a spatula until well incorporated.
Fold in the chocolate chips.
Pour the batter into the prepared pan and bake 25-30 minutes or until a toothpick inserted in the center comes out with moist crumbs clinging. Remove from the oven and allow to cool completely before frosting.
Fudge Frosting
Place chocolate chips and butter in a microwave safe bowl and microwave in 20 second increments, stirring in between, until melted.
Whisk in the vanilla and salt, then stir in the powdered sugar.
Add the milk a few drops at a time, whisking briskly, until the frosting is smooth and shiny.
Spread immediately on the cooled brownies. Refrigerate until the frosting is set and you are ready to serve. Brownies will keep wrapped tightly in plastic wrap for up to 5 days.