Heat oven to 355 degrees. Butter a 9-by-13-inch baking pan.
In a microwave-proof bowl, melt the butter and chocolate together by nuking for 30 second intervals. Stir after every interval. This should take about 2-3 minutes total microwave time. [Alternatively, use a double boiler to melt.] Let cool.
In a separate bowl, whisk together rye flour, cocoa, baking powder and sea salt.
Beat eggs, granulated and brown sugars, and vanilla until light and fluffy, about 2 minutes with an electric mixer.
Beat in chocolate-butter mixture until smooth.
Beat in flour mixture until just combined.
Pour batter into prepared pan, smoothing the top. Sprinkle lightly with flaky salt. Bake until brownies are mostly firm, with a slight wobble in the center, about 17-22 minutes.
Let cool completely before cutting into squares.
Serve within 1 day of baking or keep in refrigerator/freezer.