Place butter in a shallow 2- to 3-quart baking dish and heat in a 425° oven until melted, 3 to 4 minutes.
Meanwhile, in a blender or food processor, whirl eggs and milk until blended. Add flour and whirl until smooth, then add 1 tablespoon of the chiles and whirl just to blend. Pour batter into hot baking dish.
Bake until Dutch baby is puffed and well browned, about 20 minutes.
Meanwhile, in a bowl, mix remaining 1/2 tablespoon chiles with avocado, tomato, green onion, and lime juice.
Dust baked Dutch baby with cayenne if desired. Cut into wedges. Add avocado salsa and salt to taste.