Place the scallops into the bowl of a food processor and pulse 4 to 5 times. Add the egg whites and pulse until combined. Scrape down the sides of the bowl and add the salt, pepper, nutmeg, lemon zest, and parsley. Pulse to incorporate. With the machine running, slowly add all of the cream. Scrape down the sides of the bowl one last time, put the lid back on, and run for 5 more seconds.
Arrange the mini phyllo shells on a half-sheet pan. Place the mousse into a pastry bag or a zip-top bag with a corner snipped off and pipe into mini phyllo shells. Bake for 10 minutes. Cool the mousse cups for 2 to 3 minutes before serving.