Prep. Preheat the oven to 375°F. Line two 12-cup muffin pans with paper liners, spacing the liners out by leaving an empty cup between each one. You will use 6 cups in each pan to give the muffins plenty of room to rise and create taller, bakery-style tops. If you only have one muffin pan, you can bake the muffins in batches or bake them all at once, they just won’t get as high as a rise.
Combine the Dry Ingredients. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Rub the Sugar and Lemon Zest. In a large bowl, add the granulated sugar and lemon zest. Use your fingers to rub the zest into the sugar until the sugar is fragrant.
Mix the Wet Ingredients. Add the melted and slightly cooled butter to the lemon sugar and whisk to combine. Whisk in the eggs, Greek yogurt, milk, and vanilla extract until smooth.
Combine the Ingredients. Add the dry ingredients to the wet ingredients and stir with a spatula until just combined. Don't overmix.
Add the Blackberries. In a small bowl, gently toss the blackberries with 1 tablespoon of flour. Gently fold the blackberries into the muffin batter.
Fill and Bake. Divide the batter evenly among the prepared muffin cups, filling them almost to the top. Bake for 18 to 22 minutes, or until the tops are lightly golden and a toothpick inserted into the center comes out clean.
Cool. Let the muffins cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.
Make the Blackberry Glaze. In a small bowl, whisk together the confectioners' sugar, blackberry jam, whole milk, and fresh lemon juice until smooth.
Glaze and Serve. Spoon the blackberry glaze over the cooled muffins. Let the glaze set before serving.