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Preheat the oven to 350 degrees Fahrenheit. In a small bowl, whisk together the brown sugar, cinnamon, and cardamom and set aside.
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In a medium bowl, mix together the flour, almond meal, salt, and baking soda and set aside.
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Cream together the butter and sugar in the bowl of an electric stand mixer fitted with the paddle attachment at medium speed until smooth. Add the olive oil and continue mixing until combined. Add the eggs one at a time, mixing well after each addition.
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Add the sour cream and mix at low speed until incorporated. Then add the lemon juice, lemon zest, and vanilla extract and mix at low speed until combined (it's okay if the batter looks a little separated at this point). Add the flour mixture at low speed, stopping to scrape down the sides of the bowl as needed, until a smooth thick batter forms.
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Spray a 12-cup capacity bundt pan with baking spray and sprinkle with almond meal. Use a spoon to scoop the batter into the bundt pan just enough to make a 1-inch thick layer on the bottom of the pan. Fold the blackberries into the rest of the batter, then fill the bundt pan with 1/3 of the batter. Sprinkle half of the brown sugar mixture over the batter in the pan, then spoon another 1/3 of the batter over the top. Then sprinkle with the remaining brown sugar mixture, and top with the remaining 1/3 of the batter.
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Bake in the oven until the top of the cake is golden, the edges pull away from the sides of the pan slightly, and a toothpick inserted into the deepest part of the bundt comes out clean, about 1 hour. If the top is browning too quickly, cover it with foil and return it to the oven.
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Remove the pan from the oven and allow to cool at room temperature for 10 minutes before unmolding the bundt cake onto a wire rack. Allow the cake to cool completely, then drizzle with the blackberry glaze and serve.