Preheat your oven. Preheat the oven to 425 degrees. Be sure to grease your pan so that the muffins don't stick.
Combine dry ingredients. Grab a bowl and mix together the baking soda, baking powder, salt, and flour.
Combine wet ingredients. In a different bowl, beat softened butter on high with a mixer for about 1 minute. Now add in sugar and mix until combined well. Next, add in the eggs, vanilla, and yogurt. Beat for 1 minute on medium speed then increase to high until the mixture is combined well. About a minute more.
Mix wet and dry ingredients together. Pour dry ingredients into the wet ingredients and mix at low speed. Mix in the lemon juice, lemon zest, and milk until combined.
Add blackberries and poppyseeds. Add poppyseeds and carefully fold in the blackberries. If you stir, they're going to bleed and turn the batter purple. (it's okay if this happens but try not to let it happen). ;)
Add batter to the liners. Pour muffin batter into cupcake liners so they're about ¾ full.
Bake. Place muffins in the oven and bake at 425 degrees for 5 minutes. Once that time has passed, reduce oven temperature to 350 degrees and bake for additional 15-18 minutes.
Make the glaze. While your muffins are baking, it's time to make the glaze. On stove top in a heavy bottom pan, simmer a cup of blackberries, water, sugar and 1 tablespoon of lemon juice till it all thickens for a few minutes. Muddle the berries up and allow them to cool, then strain the reduction using a sieve to get rid of seeds. Add reduction to confectioner's sugar (a tablespoon at a time) and whisk. Add remaining lemon juice and mix it in too. Keep adding reduction, a tablespoon at a time, till a thick glaze is formed. Set aside until the muffins are done baking.
Cool the muffins down. Once muffins are done baking, let them cool down for about 10 minutes in the pan, then allow to cool down completely on a wire rack before drizzling on the glaze.