Prepare the Oven and Muffin Pan: Preheat the oven to 425°F (218°C). Line a 12-cup muffin pan with paper liners or coat it with nonstick cooking spray. Since the recipe makes up to 14 muffins, prepare a second pan if available, or plan to bake the muffins in batches. Set the pan or pans aside. Combine the Dry Ingredients: In a large mixing bowl, whisk together the all-purpose flour, poppy seeds, baking soda, baking powder, and salt until evenly distributed. Set the mixture aside.
Cream the Butter and Sugars: Using a hand mixer or a stand mixer fitted with a paddle attachment, beat the softened butter, granulated sugar, and brown sugar on medium-high speed for about 3 minutes. Continue until the mixture looks smooth, creamy, and well combined.
Mix in the Wet Ingredients: Add the room-temperature sour cream or yogurt, eggs, lemon zest, and vanilla extract to the creamed mixture. Beat on medium speed until combined. The mixture may appear slightly curdled at this stage; this is normal.
Finish the Muffin Batter: Add the dry ingredient mixture and beat on low speed until it is almost incorporated. Pour in the milk and fresh lemon juice, then continue mixing on low speed until the ingredients are combined. The finished batter should be thick.
Fold in the Blackberries: Gently fold the blackberries into the batter using a rubber spatula. If using frozen berries, add them without thawing. For especially juicy blackberries, follow the layering method in the recipe notes to help prevent the batter from becoming purplish-gray. Fill the Muffin Cups: Divide the batter evenly among the prepared muffin cups, filling each liner all the way to the top. If baking in batches, keep the remaining batter ready for the next batch.
Bake the Muffins: Bake at 425°F (218°C) for 5 minutes. Without removing the muffins from the oven, reduce the temperature to 350°F (177°C) and bake for another 16–18 minutes. The muffins are ready when a toothpick inserted into the center comes out clean. Total baking time should be approximately 21–23 minutes. Cool the Muffins: Let the muffins rest in the pan for 5 minutes after baking. Carefully transfer them to a wire rack and allow them to continue cooling.
Prepare the Lemon Blackberry Icing: In a small bowl, whisk together the sifted confectioners’ sugar, lemon juice, and milk until smooth. Add the blackberry jam and whisk until evenly incorporated. If using fresh blackberries instead, mash 3–4 berries with a fork and whisk them into the icing. For a thicker consistency, add 2–3 additional tablespoons of sifted confectioners’ sugar, if desired. Ice the Muffins: Drizzle the lemon blackberry icing over the warm or cooled muffins. Allow the icing to settle before serving.
Store the Muffins: Once prepared, keep the muffins covered at room temperature for a few days or refrigerate them for up to 1 week. For longer storage, freeze the baked, cooled muffins for up to 3 months, preferably without icing. Thaw them in the refrigerator or at room temperature, then add fresh icing before serving.
