Preheat your oven to 375°F (190°C), and line a muffin tin with paper liners or grease it lightly.
In a large mixing bowl, whisk together the sifted all-purpose flour, sugar, baking powder, baking soda, and salt until well combined.
In another bowl, whisk together the Greek yogurt, milk, vegetable oil, and egg until smooth and creamy.
Pour the wet mixture into the dry ingredients and gently fold together using a spatula until just combined. Don't overmix—some lumps are fine.
Carefully fold in the fresh blackberries, distributing them evenly throughout the batter without breaking them apart.
In a small bowl, prepare the crumb topping by mixing brown sugar, flour, and cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs.
Spoon the muffin batter evenly into the prepared muffin tin, filling each cup about three-quarters full.
Sprinkle the crumb mixture generously over each muffin, adding a crunchy, buttery topping on top of the moist batter.
Bake the muffins in the preheated oven for about 20–25 minutes, or until the tops are golden brown and a toothpick inserted in the center comes out clean.
Remove the muffins from the oven and let them cool slightly in the tin for about 5 minutes before transferring to a wire rack.
Enjoy these muffins warm or at room temperature, with the crunchy topping and juicy berries adding delicious textures and flavors to each bite.