Adjust oven rack to mniddle position and heat oven to 350 degrees. Put chocolate and butter in microwave proof bowl. Microwave for 2 minutes at 50% power. Stir; continue microwaving at 50% power for another minute. Stir; continue microwaving at 50% power for a final minute. Cool.
Whisk flour, baking powder and salt together in a small bowl; set aside
Whisk sugar into cooled chocolate mixture. Whisk in eggs and vanilla, then fold in flour mixture until just combined.
Pour batter in to greased 8x8" metal baking dish; bake until toothpick comes out iwth a few fudgy crumbs, 20 minutes.