Step 1: Heat oven to 350 degrees. Butter a 9-by-13-inch baking pan.
Step 2: Using a double boiler, or in a metal bowl set over a saucepan containing an inch of simmering water (do not let bottom of bowl touch the water), melt the butter and chocolate, stirring with a heatproof rubber spatula. Let cool.
Step 3: In a separate bowl, whisk together rye flour, cocoa, baking powder and sea salt.
Step 4: Using an electric mixer, beat eggs, granulated and brown sugars and vanilla until light and fluffy, about 2 minutes. Beat in melted chocolate mixture until smooth. Beat in flour mixture.
Step 5: Pour batter into prepared pan and smooth the top. Sprinkle lightly with flaky salt and bake until brownies are mostly firm, but with a very slight wobble in the center, about 25 minutes. (Note that a tester inserted in the center will not come out clean.) Let cool completely before cutting into squares.
Step 6: Serve within 1 day of baking.
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