Serves 10 to 12
1. For the eggs: Adjust oven rack to middle position and heat oven to 375 degrees F. Line 18-inch by 13-inch rimmed baking sheet with 18-inch by 16-inch sheet of aluminum foil, folding excess over sides of sheet, and spray foil and sides of sheet liberally with vegetable oil spray. Top foil with two 16-1/2 inch by 13-1/2 inch sheets of parchment paper, allowing parchment to overhang one long edge of baking sheet by 1 inch. Spray parchment liberally with vegetable oil spray.
2. Combine flour, butter, salt and pepper in bowl and mash with fork to make smooth paste. Bring milk to boil in medium saucepan. Reduce heat to medium-low, whisk in flour mixture, and simmer, whisking constantly, until thickened, about 2 minutes. Off heat, whisk in Parmesan; reserve 1/3 cup of milk mixture. Scrape remaining milk mixture into large bowl, let sit until slightly cooled, about 10 minutes, and then whisk in egg yolks.
3. Using stand mixer fitted with whisk, whip egg whites and cream of tartar on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip until stiff peaks form, 3 to 4 minutes. Gently fold one-third of beaten egg whites into milk-yolk mixture. Using rubber spatula, fold in remaining egg whites until no white streaks remain. Spread mixture onto prepared baking sheet. Bake until golden brown and set, 22 to 24 minutes. Let cool in pan for 30 minutes. Reduce oven to 325 degrees F.
4. For the filling: Combine reserved milk mixture, spinach, Gruyere, chives, milk, pepper and salt in bowl and microwave until hot, 1 to 2 minutes. Spread spinach filling evenly over cooled egg sheet. Using parchment overhang, lift long edge of egg sheet and roll to opposite edge (parchment should encase roulade when rolling). With roulade still resting on edge of parchment, pull roulade to center of baking sheet, and finally roll it off seam side down onto foil; discard parchment.
Cover roulade with foil, and bake until hot throughout, about 25 minutes. Slice into 1-inch-thick slices and serve.
To make ahead: Roulade can be prepared through step 4, wrapped in plastic wrap, and refrigerated for up to 24 hours. To serve, discard plastic and proceed with step 5, increasing baking time to 35 minutes.