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Position a rack in the lower third of the oven and preheat to 350ºF. Butter a 9 by 5-inch loaf pan and line the bottom and sides with parchment paper.
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Make the cake: In the bowl of a stand mixer fitted with the paddle attachment or in a large bowl with a spoon, beat together the butter, cream cheese, granulated sugar, and lemon zest until light and fluffy, 3 to 5 minutes. Add the eggs one at a time, beating to incorporate each, then beat in the lemon juice.
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In a bowl, sift together the flours, baking powder, and salt. Add this mixture to the butter mixture and beat on medium-low until well combined, scraping down the sides as needed.
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Remove the bowl from the mixer and fold in the berries. Scrape the batter into the prepared pan, smooth the top with a spoon, and bake until deeply bronzed on top and a knife inserted into the center comes out with just a few moist crumbs, 65 to 75 minutes. If the cake is browning too quickly, decrease the oven temperature by 25ºF.
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Let cool 10 minutes, then gently turn out of the pan, place on a wire rack, and let cool to warm.
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Meanwhile, make the glaze: whisk together the lemon zest, powdered sugar, salt, and enough lemon juice to make a glaze the consistency of heavy cream.
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Transfer the cake to a rimmed dish, then use a pastry brush to pour and brush the glaze all over the top and sides of the warm cake. Let the cake cool completely, then slice and serve.