Bakery-style muffins with tall, tender domes bursting with juicy blackberries, bright lemon zest, and crunchy poppy seeds, finished with a tangy lemon-blackberry drizzle. Moist, fluffy crumb thanks to creamed butter and Greek yogurt or sour cream.
Preheat oven to 425°F (218°C). Grease a 12-count muffin pan or line with paper liners; you may need a second pan for up to 14 muffins.
Whisk dry ingredients: in a large bowl combine flour, poppy seeds, baking soda, baking powder, and salt; set aside.
Cream butter and sugars: using a handheld or stand mixer fitted with the paddle, beat the butter, granulated sugar, and brown sugar on medium-high until smooth and creamy, about 3 minutes.
Add wet ingredients: beat in sour cream (or plain yogurt), eggs, lemon zest, and vanilla on medium speed until combined (mixture may look curdled).
Add dry, then liquids: on low speed mix in the dry ingredients until almost combined. Add milk and lemon juice and beat on low just until combined; batter will be thick.
Fold in blackberries gently. If berries are very juicy, you can layer: fill cups halfway, add a few berries, top with more batter, then lightly swirl; press a few berries on top if desired.
Divide batter among muffin cups, filling each to the top.
Bake 5 minutes at 425°F (218°C). Without opening the oven, reduce temperature to 350°F (177°C) and bake 16–18 minutes more, or until a toothpick comes out clean (about 21–23 minutes total).
Cool muffins in the pan for 5 minutes, then transfer to a wire rack to cool slightly or completely.
Make the icing: whisk confectioners’ sugar, lemon juice, and milk until smooth. Whisk in blackberry jam or mashed fresh blackberries; add 2–3 more tablespoons confectioners’ sugar to thicken if desired.
Drizzle icing over warm or cooled muffins and serve.
Storage: Cover and store at room temperature for a couple of days or refrigerate up to 1 week. Freeze (preferably without icing) up to 3 months; thaw before icing/serving.