1. Preheat oven to 400°. Heat a 10-inch cast-iron skillet in oven. Trim roots from onions; discard roots. Chop half of onions.
2. 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.
3. 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.
4. 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.) Serve immediately.