Preheat the oven to 425°F (220°C) and line a standard 12-cup muffin pan with paper liners.
Whisk the flour, baking powder, baking soda, and salt together in a large bowl.
In a separate bowl, whisk the melted butter and granulated sugar together.
Add the eggs and vanilla and whisk until combined.
Add the sour cream and milk and mix until mostly smooth.
Pour the wet ingredients into the dry ingredients and gently fold together until just combined. Do not overmix.
Fold in most of the chocolate chips, reserving a small handful for the tops.
Divide the thick batter generously between the 12 muffin cups.
Scatter the remaining chocolate chips over the muffins and sprinkle with coarse sugar if desired.
Bake at 425°F (220°C) for 5 minutes.
Without opening the oven door, reduce the temperature to 350°F (175°C).
Continue baking for 14–17 minutes, until the muffins are golden and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool in the muffin pan for 5 minutes before transferring to a wire rack.
Serve slightly warm or at room temperature.