Stir together first 5 ingredients until well blended.
Remove 1/4 cup mixture, and wrap in plastic wrap; chill. Press remaining cheese mixture into a 6-cup or 5-liter plastic wrap-lined bowl. Cover and chill 2 hours.
Remove plastic wrap from chilled 1/4 cup cheese mixture. Shape heaping teaspoonfuls of cheese mixture into eggs. Chill until ready to serve.
Unmold cheese mixture; remove plastic wrap, and place on a serving platter. Press a 2-inch indention into center of cheese mold. Press thyme sprigs around top edge and sides of mold to resemble a nest. Arrange eggs in center of nest.
