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Preheat the oven to 350°F (180°C) and line a 9x13-inch (23x33-cm) baking pan with aluminum foil. Butter the foil and set aside.
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In a medium bowl, mix together the coconut and condensed milk. Set aside.
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In another small bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.
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In a stand mixer fitted with a paddle attachment (or in a medium bowl with a handheld electric mixer) beat together the butter and sugar until fluffy, about 3 minutes.
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Add the eggs, one at a time and scraping down the sides of the bowl after each addition, then fold in the flour mixture.
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Spread half of the brownie batter in the prepared pan. Carefully spread the coconut mixture on top, then spread the remaining brownie batter on top of the coconut.
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Bake for about 60 minutes, until firm and a skewer inserted in the center comes out with a few moist crumbs attached but no wet batter.
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Let cool completely in the pan before cutting into squares.
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Store in an airtight container at room temperature for up to 3 days.