Preheat the Oven:
Preheat your oven to 350°F (175°C). Grease a 9×5-inch loaf pan and line with parchment paper.

Cream Butter and Sugar:
In a large mixing bowl, beat the softened butter and sugar together until light and fluffy (about 3–4 minutes).

Add Eggs and Flavorings:
Add the eggs one at a time, beating well after each addition. Mix in lemon zest, lemon juice, and vanilla extract.

Combine Dry Ingredients:
In a separate bowl, whisk together flour, baking powder, and salt.

Mix Batter:
Add half of the dry ingredients to the wet ingredients, mix gently. Add Greek yogurt and mix. Add the remaining flour mixture and mix until just combined—don’t overmix.

Fold in Blackberries:
Toss the blackberries with 1 teaspoon of flour (to prevent sinking), then gently fold into the batter.

Bake:
Pour the batter into the prepared loaf pan and smooth the top. Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean.

Cool and Glaze:
Let the cake cool in the pan for 15 minutes, then transfer to a wire rack.
If glazing, whisk powdered sugar and lemon juice together, then drizzle over the cooled cake.