Preheat the oven to 425 degrees F. Place the butter in a 9x13 baking dish and stick it in the oven while you prepare the other ingredients.
In a blender, combine the eggs, milk, salt, chives, flour and about ½ cup of the cheese. Blend until smooth and combined.
Bring the dish out of the oven (the butter should be melted! If not, wait until it melts.). Pour the batter into the hot pan.
Return the pan to the oven and bake for 25 minutes, until the pancake is puffed up and golden.
While it bakes, crisp up the prosciutto. Heat a nonstick skillet over medium heat. Add the prosciutto in a single layer. Let it cook for 2 to 3 minutes, until it gets darker in color, then flip it. Let it cook for 2-3 minutes more. Remove and let it cool on a plate.
As soon as the pancake is done, top with the remaining cheese. Let it melt fully. Crush the prosciutto over the dutch baby and add the fresh herbs.
Slice and serve!