• Preheat the oven at 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 the blueberries if fresh, or use directly from the freezer but make sure they are not clumped. 

For the cake:

1. Beat soft butter for 20 seconds in a large bowl with electric beaters or a stand mixer with the paddle attachment. 
2. Add both sugars gradually while you continue beating at medium speed, and then for 2 more minutes after adding all of it. The mixture should be light in color, fluffy and the sugar will have partially dissolved. 
3. Add the eggs, one at a time, beating well after each addition. Make sure to scrape the sides of the bowl regularly. 
4. Add vanilla, lemon zest, lemon juice and mix. It might look curdled, but don't worry.
5. Sift the dry ingredients (flour, salt and baking powder) together in a bowl, or have them measured and sift them directly over the cake batter (how I do it). 
6. Add them in 2 parts, alternating with the yogurt in 1 part. That means you start and end with the dry ingredients. 
7. 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 cake.
8. 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. 
9. Pour batter into the prepared pan and smooth the top. 
10. 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.
11. Cool on a wire rack and remove carefully from the pan, removing the strip of paper. 
12. Drizzle the glaze (instructions below) over the completely cooled loaf and let it drip down the sides.
13. Add some blackberries and lemon zest before it dries out if you want to.
14. Let it dry before cutting and eating. 
15. 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:

1. Put a small bowl with a colander on top, add the 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 a full tablespoon. 
2. Put the powdered sugar in a bowl and add the liquid.
3. Check the consistency. It should be like thick honey. Add more juice if needed to adjust the consistency. 
4. Pour over the cooled cake and let drip down the sides. Let dry before cutting.