Rinse mushrooms; trim and discard discolored stem ends. With a knife or in a food processor, finely chop mushrooms. Put mushrooms and butter in a 10- to 12-inch frying pan over medium-high heat. Cover and stir occasionally until juicy, about 3 minutes. Uncover and stir often over high heat until mushrooms are lightly browned, about 15 minutes.
Add broth and couscous to mushrooms; stir, cover, and remove from heat. Let stand 10 minutes. Stir couscous and season to taste with salt. Use hot or cool. If making up to 2 hours ahead, cover and let stand at room temperature; stir with a fork before using. Spoon couscous mixture equally into 6 ramekins (2 3/4 to 3 in. wide, 1 3/4 to 2 in. deep).
In a bowl with a mixer on high speed, whip cream until it holds soft peaks. Spoon cream equally into ramekins. Break 1 egg onto cream in each ramekin, then sprinkle equally with cheese. Sprinkle nutmeg lightly over cheese. Set ramekins slightly apart in a rimmed pan (9 by 13 or 10 by 15 in.).
Bake in 450° regular or convection oven until yolks are softly set (press gently with tip of a spoon to test), 8 to 10 minutes, or until firm, 12 to 14 minutes. Serve with spoons. Add salt to taste.