Heat a 10-inch cast-iron skillet in oven. Trim roots from onions; discard roots. Chop half of onions.
Whisk together eggs and milk. Sift together flour and next 3 ingredients. Gradually add flour mixture to egg mixture, whisking rapidly 20 to 30 seconds or just until blended and smooth. (There should be no lumps.) Stir in chopped onions.
Let stand 5 minutes.
Carefully remove hot skillet from oven.
Add butter, and let stand until butter is melted.
Place skillet over medium-high heat, and pour batter into skillet. Arrange cheese and remaining whole onions over top of batter, and cook 30 seconds to 1 minute or until edges begin to set.
Transfer skillet to top oven rack, and bake at 400 for 22 to 25 minutes or until golden brown and puffy. (Outside edges should be crispy, and inside texture should resemble a custard popover. Pie will deflate quickly.)
