Preheat the oven to 350 degrees F. Place the eggs in a bowl and beat until the yolks and whites are well blended. Mix in the milk, cream, tarragon, salt, white pepper and nutmeg. Place half the Swiss, Jarlsberg and Brie cheeses in the pie crust. Top the cheese with 3/4 of the spinach. Top the spinach with the remaining cheese. Pour in the egg mixture. Arrange the shrimp and remaining spinach on top of the quiche, gently pushing them into the egg mixture. Bake 45 to 50 minutes, or until eggs are set. Rest the quiche 10 minutes to allow the filling to set before slicing.