1. Adjust oven rack to middle position and heat oven to 500° F.
2. Melt butter in medium saucepan over medium heat. Add shallot and cook, stirring occasionally, until softened, about 3 minutes. Stir in flour and cook, stirring constantly, for 1 minute. Gradually whisk in half-and-half; bring mixture to boil, whisking constantly. Simmer, whisking frequently, until thickened, 2 to 3 minutes. Remove pan from heat and stir in spinach, Parmesan, ¾ teaspoon salt, ½ teaspoon pepper, mustard, nutmeg, and cayenne.
3. Lightly spray six 6-ounce ramekins with oil spray. Evenly divide spinach filling among ramekins. Using the back of a spoon, push filling 1 inch up the sides of the ramekins to create 1/8-inch-thick layer. Shape remaining filling in bottom of ramekin into 1½-inch diameter mound, making shallow indentation in center of mound large enough to hold yolk. Place filled ramekins in 13 by 9-inch glass baking dish. Bake until filling just starts to brown, about 7 minutes, rotating dish halfway through baking.
4. While filling is heating, crack eggs (taking care not to break yolks) into individual cups or bowls. Remove dish with ramekins from oven and place on wire rack. Gently pour eggs from cups into hot ramekins, centering yolk in filling. Lightly spray surface of each egg with oil spray and sprinkle each evenly with pinch salt. Return dish to oven and bake until whites are just opaque but still tremble (carryover heat will cook whites through), 6 to 8 minutes, rotating dish halfway through baking.
5. Remove dish from oven and, using tongs, transfer ramekins to wire rack. Let stand until whites are firm and set (yolks should still be runny), about 10 minutes. Serve immediately.
Chef's Notes:
In order for the eggs to cook properly, it is critical to add them to the hot filling–lined ramekins quickly. Use 6-ounce ramekins with 3¼-inch diameters, measured from the inner lip. It is imperative to remove the eggs from the oven just after the whites have turned opaque but are still jiggly—carryover cooking will finish the job. We developed this recipe using a glass baking dish; if using a metal baking pan, reduce the oven temperature to 425 degrees. This recipe can be doubled. If doubling, bake the ramekins in two 13 by 9-inch dishes and increase the baking times in steps 3 and 4 by 1 minute.
TO MAKE AHEAD
Follow recipe through step 3, skipping baking of lined ramekins. Wrap ramekins with plastic wrap and refrigerate for up to 3 days. To serve, remove plastic and heat lined ramekins, directly from refrigerator, for additional 3 to 4 minutes (10 to 11 minutes total) before proceeding with recipe.