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1
Heat the oven to 400 degrees F and arrange a rack in the middle.
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2
Generously coat a 13-by-9-inch baking dish with butter, then evenly sprinkle the bottom and sides with 1/2 cup of the Parmesan; set aside.
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3
Bring the water to a simmer in a large frying pan over medium heat.
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4
Add the broccoli, season with salt and pepper, and stir to combine.
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5
Cover with a tightfitting lid and cook, stirring occasionally, until the broccoli is crisp-tender, about 10 minutes.
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6
Meanwhile, line a baking sheet with a double layer of paper towels.
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7
When the broccoli is ready, drain it in a colander.
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8
Transfer it to the prepared baking sheet, spread it into an even layer, and set aside.
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9
Wipe out the frying pan with paper towels, add the measured butter, and melt over medium heat.
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10
Add the onion and cook, stirring occasionally, until softened, about 10 minutes.
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11
Add the flour, measured salt, and measured pepper and cook, stirring often, until the flour has darkened slightly in color, about 5 minutes.
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12
While whisking constantly, slowly add the milk to the flour mixture until evenly combined and smooth.
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13
(It will get very thick when you first add the milk, then thin out.)
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14
Increase the heat to medium high and cook, whisking occasionally, until the mixture comes to a full simmer and thickens slightly, about 5 minutes.
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15
Remove the pan from the heat and whisk in the remaining 2 cups of Parmesan.
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16
Whisk in the egg yolks until smooth and combined.
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17
Transfer the Parmesan sauce to a large bowl.
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18
Transfer the reserved broccoli to a food processor fitted with a blade attachment and add 1/2 cup of the Parmesan sauce.
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19
Process, stopping and scraping down the sides of the food processor as necessary, until smooth, about 1 minute.
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20
Transfer the broccoli mixture to the bowl with the Parmesan sauce and stir to combine.
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21
Taste and season with salt and pepper (the mixture should be slightly salty); set aside.
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22
Place the egg whites and cream of tartar in the bowl of a stand mixer fitted with a whisk attachment.
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23
Whisk on high speed until stiff peaks form, about 2 minutes.
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24
Transfer about a third of the egg whites into the broccoli mixture and stir with a rubber spatula to incorporate.
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25
Add the remaining egg whites and gently fold until thoroughly combined and no big streaks of egg white remain, being careful not to overmix.
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26
Transfer the mixture to the prepared baking dish and spread it into an even layer.
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27
Bake until puffed, golden brown, and just set, about 40 minutes.
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28
Serve immediately.