The recipe gives a range of baking times—use the shorter time for metal pans, the longer for Pyrex pans.
Position an oven rack on the middle rung. Heat the oven to 350°F. In a double boiler over simmering water, melt the chocolate. Remove the pan from the heat; cool slightly. Butter an 8-inch square pan, line the pan bottom with parchment (or waxed paper), and then butter the parchment.
In a medium bowl, cream the butter with a fork. Beat in the sugar and corn syrup; be sure there are no lumps in the mixture. Add the eggs, one at a time, whisking thoroughly. Add the vanilla and milk. Whisk until incorporated, about 30 seconds. The batter may appear broken; this is okay. Whisk in the melted chocolate, beating until the batter is smooth and has thickened slightly, 30 to 60 seconds. Stir together the flour, baking powder, and salt so they're well blended; stir the dry ingredients into the chocolate mixture until incorporated. Scrape into the prepared pan and bake until a toothpick inserted in the middle comes out clean with a few moist crumbs clinging to it, 20 to 30 minutes.
Set the pan on a rack until cool enough to handle. Run a paring knife around the inside edge of the pan and then invert the pan onto a flat surface and peel off the parchment. Flip the baked brownie back onto the rack to cool completely. Cut into squares with a sharp knife.