Preheat the oven to 425°F (220°C). Line a 12-cup muffin tin with paper liners or lightly grease each cup.
In a large bowl, combine the granulated sugar and lemon zest. Use your fingers to rub the zest into the sugar until fragrant and well incorporated—this enhances the citrus flavor.
Add the eggs to the lemon sugar and whisk for 2–3 minutes, until the mixture is pale and slightly thickened.
Whisk in the melted butter, followed by the buttermilk, sour cream, vanilla bean paste, and oil. Mix until the wet ingredients are smooth and fully combined.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Remove 2 tablespoons of the flour mixture and toss with the mixed berries to prevent them from sinking during baking.
Gently fold the wet mixture into the dry ingredients just until combined. Do not overmix.
Fold in the floured berries, being careful not to crush them.
Cover the batter and let it rest at room temperature for 30 minutes—this helps create tall, bakery-style muffin tops.
Divide the batter evenly among the muffin cups, filling each about 3/4 full. Top with extra berries, if desired.
Cool the muffins in the tin for 5 minutes, then transfer to a wire rack to cool completely.
