Preheat your oven to 375°F (190°C) and line a muffin tin with paper liners.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt until evenly combined.
Cut cold butter into small cubes and add to the flour mixture. Use a pastry cutter or fork to incorporate the butter until the mixture resembles coarse crumbs.
In a separate bowl, whisk together the eggs, buttermilk, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently fold with a spatula until just combined; do not overmix.
Gently fold in the blackberries and chopped rhubarb, distributing them evenly throughout the batter.
Spoon the batter into the prepared muffin liners, filling each about 3/4 full to leave space for rising.
In a small bowl, combine additional flour, sugar, and cold butter to make the crumble topping. Use your fingers or a fork to mix until crumbly.
Sprinkle the crumble evenly over each muffin, pressing down lightly to help it adhere.
Bake the muffins for about 22-25 minutes, or until they are golden brown and a toothpick inserted in the center comes out clean.
Remove from oven and let the muffins cool in the pan for 5 minutes before transferring to a wire rack to cool completely. Enjoy the warm, fragrant aroma and juicy bites.
