Preheat the oven to 350F degrees and line 2 muffin pans with liners. You'll end up with about 14 cupcakes in total.

In a large bowl sift together the flour, baking powder, baking soda and salt. Give them a whisk.

In a separate large bowl, beat the butter, sugar and lemon zest until fluffy.

Beat in the eggs and vanilla extract.

With the mixer on low speed, beat in about 1/2 of the sour cream followed by about 1/2 of the flour mixture. Turn off the mixer and scrape down the sides of the bowl. Repeat the process with the rest of the sour cream and flour mixture.

Gently fold in the lemon juice and poppy seeds.

Spoon the batter into the prepared muffin pans filling each about 2/3 full. You should get about 14 cupcakes.

Bake for 16-20 minutes, or until the tops look set and an inserted toothpick comes out clean. Cool in the pan for at least 10 minutes, then continue cooling on a wire rack.

Add the blackberries to a blender or food processor and blend until smooth. Press the puree through a sieve to remove the seeds and transfer to a small-medium saucepan over low heat. Simmer until thick.

In a large bowl, beat the butter until soft. Beat in powdered sugar and salt, then incorporate blackberry puree to taste. Adjust consistency with additional powdered sugar or cream as needed.

Transfer the frosting to a piping bag to frost the cupcakes, or use a knife to frost.