Preheat your oven to 400°F. Line a 12-cup muffin tin with paper liners and set aside.
Prepare the wet mixture. In a large mixing bowl, mash the bananas with a fork until smooth. Add the eggs, oil, Greek yogurt, brown sugar, vanilla extract, and lemon zest. Whisk everything together until fully combined and smooth.
Mix the dry ingredients. In a separate medium bowl, whisk together the flour, baking powder, baking soda, ground cardamom, and kosher salt. Whisk for about 10 seconds to ensure the leavening agents are evenly distributed.
Combine wet and dry ingredients. Pour the dry mixture into the wet mixture. Using a silicone spatula, gently fold the ingredients together until just combined. You should still see a few flour streaks in the batter. Do not overmix or your muffins will turn out dense.
Coat and fold in the blackberries. Place the blackberries in a small bowl and sprinkle 1 tablespoon of flour over them. Toss gently to coat. Fold the coated blackberries into the batter using just a few gentle strokes.
Fill the muffin cups. Divide the batter evenly among the 12 muffin cups, filling each one almost to the top (about 90% full). This ensures tall, domed muffin tops.
Bake using the two-temperature method. Place the muffin tin in the preheated oven and bake at 400°F for 5 minutes. After 5 minutes, reduce the oven temperature to 375°F without opening the oven door. Continue baking for an additional 15 to 17 minutes, or until a toothpick inserted into the center of a muffin comes out clean or with just a few moist crumbs.
Cool the muffins. Remove the muffin tin from the oven and let the muffins cool in the pan for 5 minutes. Then transfer them to a wire cooling rack to cool completely.