Preheat oven to 425° with a rack in center and another beneath it. In a blender, whirl eggs, milk, and salt to break up. Add flour and whirl until smooth.
Divide butter among 12 muffin cups (1/3-cup size). Bake on center rack in oven until butter melts and begins to brown, 2 to 3 minutes. Pour batter into cups and sprinkle with chiles and cheese. Set on center rack and put a rimmed baking sheet beneath to catch any drips. Bake until Dutch babies are very well-browned and puffed, 18 to 20 minutes.
Loosen from pan with a knife and spoon. Serve immediately, with salsa.