• Preheat the oven to 350°F (180°C).
• Butter or spray a 9x4 inch (10x24 cm) loaf pan and, if you want, add a strip of parchment paper to cover the bottom and two shorter sides. The long sides will remain unlined. This will make it easier to remove the cake. 
• Wash and dry 2 cups blackberries if they are fresh, or use them directly from the freezer, but make sure they are not clumped. 

For the cake:

• Beat ¾ cup unsalted butter at room temperature for 20 seconds in a large bowl with electric beaters or a stand mixer with the paddle attachment. 
• Add ⅓ cup white granulated sugar and ½ cup brown sugar gradually while you continue beating at medium speed, and then beat for 2 more minutes after adding all of it. The mixture should be light in color, fluffy and the sugars will have partially dissolved. 
• Add 4 eggs, one at a time, beating well after each addition. Make sure to scrape the sides of the bowl regularly. 
• Add ½ teaspoons pure vanilla extract, 1 tablespoon lemon zest and 1 tablespoon fresh lemon juice and mix. It might look curdled, but don't worry.
• Sift the dry ingredients (2 ¼ cups all-purpose or cake flour, 1 teaspoon baking powdert and ¼ teaspoon salt) together in a bowl, or have them measured and sift them directly over the cake batter (how I do it). 
• Add them in 2 parts, alternating with ½ cup Greek yogurt in 1 part. That means you start and end with the dry ingredients. Mix and integrate everything well, but don't beat much at this point. After adding the last part of the flour mixture, don't incorporate it fully so you have dry spots when you add the berries. After adding the flour, cake batters should be beaten on low speed *just* until integrated, but not overmixed, as that will develop gluten and toughen the baked loaf.
• Add the blackberries and lightly fold them into the batter with a spatula. Make sure everything is incorporated and try not to crush the fruit. But make sure there are no flour spots. You should have a thick, smooth batter with berries. If some of them break and color the batter, that's fine. 
• Pour batter into the prepared pan and smooth the top. 
• Bake in the middle rack for about 45 minutes, until it rises, the top cracks, and a cake tester or toothpick inserted in the middle comes out clean. If the top is browning too quickly but the middle is not done, cover the top of the bread loosely with a piece of aluminum foil and continue to bake.
• Cool on a wire rack and remove carefully from the pan, removing the strip of paper. 
• Drizzle the glaze (instructions below) over the completely cooled loaf and let it drip down the sides. Add some extra fresh blackberries and lemon zest before it dries out if you want to. Let it dry before cutting and eating. 
• Add some blackberries and lemon zest before it dries out if you want to. Let it dry before cutting and eating. 
• Let it dry before cutting and eating. 
• Keep leftovers at room temperature for a day or in the refrigerator for several days, with plastic wrap in both cases or in an airtight container. Or frozen for a month, also well wrapped. 

For the glaze:

• Place a small bowl with a colander on top, add 6 or 7 blackberries and crush them with a fork. The juice will be collected in the bowl. Measure it in a 1 tablespoon measuring spoon and add enough lemon juice to make 2 tablespoons. Alternatively, use 1 ½ tablespoon blackberry juice from a bottle with ½ tablespoon lemon juice to make the needed two tablespoons.
• Mix 1 cup powdered sugar with the liquid in a small bowl until smooth. Check the consistency. It should be like thick honey. Add more juice if needed to adjust the consistency.