1. Place butter in a shallow 2- to 3-quart baking dish and heat in a 425° oven until melted, 3 to 4 minutes.
2. 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.
3. Bake until Dutch baby is puffed and well browned, about 20 minutes.
4. Meanwhile, in a bowl, mix remaining 1/2 tablespoon chiles with avocado, tomato, green onion, and lime juice.
5. Dust baked Dutch baby with cayenne if desired. Cut into wedges. Add avocado salsa and salt to taste.