Position an oven rack in the center and preheat the oven to 425 degrees F.
Add milk, flour, sugar, eggs, nutmeg, and salt to a medium bowl. Whisk well to make a smooth batter. If using fresh blueberries, add them to the batter and stir gently. (If using frozen blueberries, add them to the pan after pouring in the batter, see step #4.)
On the stove top, melt the butter over low to medium heat in a 10-inch ovenproof pan. Tilt the pan so butter coats entire bottom and a bit up the sides.
Pour the batter into the pan. If using frozen blueberries, add them to the batter in the pan. Use a spoon to distribute the blueberries and give the pan a gentle shake to evenly distribute the batter. Don't worry about any butter that pooled up and over the batter.
Transfer the pan to center rack in the oven and bake for 12-15 minutes (14 - 17 minutes if using frozen blueberries) until pancake is set, puffed, and golden brown around the edge. The Dutch Baby will begin to deflate soon after removal from the oven. Slice and serve immediately.