Preheat the oven to 350°F (175°C) and prepare a 9x5-inch loaf pan by greasing it or lining it with parchment paper.

In a large mixing bowl, cream together the unsalted butter and granulated sugar until light and fluffy, about 3–4 minutes.

Add the eggs one at a time, mixing well after each addition, then stir in lemon zest, lemon juice, and vanilla extract.

In a separate bowl, whisk together the flour, baking powder, and salt, then set aside.

Gradually mix the dry ingredients into the wet mixture, alternating with Greek yogurt, until just combined.

Toss the blackberries with flour to prevent sinking, then gently fold them into the batter.

Pour the batter into the prepared pan and bake for 50–60 minutes or until golden brown and a toothpick comes out clean.

Allow the cake to cool in the pan for about 15 minutes before transferring it to a wire rack. Whisk powdered sugar and lemon juice to make a glaze and drizzle over the cooled cake.