Preheat the oven to 425°F.
Line a 12-cup muffin pan with paper liners, or grease each cup well.
Whisk flour, baking powder, baking soda, and salt in a medium bowl.
In a large bowl, whisk melted butter, oil, granulated sugar, and brown sugar.
Add eggs and vanilla, then whisk until smooth.
Whisk in sour cream and milk until the mixture looks even.
Add the dry ingredients to the wet ingredients.
Use a spatula to fold the batter gently.
Stop when a few flour streaks still remain.
Add 1 1/4 cups chocolate chips and fold a few more times.
Divide batter evenly among the muffin cups.
Fill each cup almost to the top.
Sprinkle extra chocolate chips and coarse sugar over the tops.
Bake at 425°F for 5 minutes.
Without opening the oven, reduce the heat to 350°F.
Bake for 13 to 16 more minutes.
Use a toothpick to check the centers.
Look for moist crumbs, not wet batter.
Avoid hitting a melted chocolate chip when checking.
Cool in the pan for 5 minutes.
Move the muffins to a wire rack.
Let the muffins cool slightly before serving.