Preheat the oven to 425°F (218°C). Line a mini muffin pan with paper liners and set it aside.
Melt the butter in a medium bowl in the microwave. Set the melted butter aside to cool slightly while you move on to the next step.
In another medium bowl, add flour, baking powder, baking soda, and salt and whisk to combine. Set aside.
To the melted butter add vegetable oil, both sugars, and lemon zest. Whisk to combine.
Add egg and whisk to combine.
Add sour cream, milk, and vanilla and whisk one more time until the mixture is well blended.
Add the flour mixture to the liquid mixture and gently fold the dry ingredients into the wet ingredients just until blended. Do not over mix the batter.
Add the blueberries to the muffin batter and fold the berries into the batter just until well distributed.
Divide the muffin batter evenly into the prepared muffin pan so that each liner is ¾ full.
Bake the muffins at 425°F (218°C) for 4 minutes, then turn down the oven temperature to 350°F (177°C), keeping the muffins in the oven and without opening the oven door. Continue to bake the muffins until the tops are golden and spring back when gently poked, about 10-12 minutes more.
Let the muffins cool in the pan on a wire rack for 10 to 15 minutes. Then carefully remove the still-warm muffins from the pan and transfer them to the wire rack to cool completely.