Step 1Heat the oven to 425 degrees. In a large, heavy-bottom saucepan, bring the water, milk, butter, salt and sugar to a boil. Quickly stir in the flour, making sure to remove any lumps. Reduce the heat to low and continue to stir until the mixture forms a thin film on the bottom of the pan, 2 to 3 minutes. Remove from heat.
Step 2Transfer the mixture to the bowl of a stand mixer and beat with the paddle attachment on medium speed until the mixture cools. With the mixer running, beat in the 5 whole eggs, one at a time, until fully incorporated.
Step 3Transfer the dough to a large piping bag fitted with a medium (one-half inch) round tip. The batter will make about 1 1/2 dozen large (2 inches wide by 1 inch high) round buns for the base and 1 1/2 dozen small (1 inch wide by 1 inch high) round buns for the top. Pipe the buns out on parchment-lined baking sheets. You will need two baking sheets, one each for the large and small buns. Space the buns about 2 inches apart for the larger buns and 1 1/2 inches apart for the smaller buns.
Step 4Thin the remaining egg white with a tablespoon of water to make an egg wash and very gently brush the wash over the buns. Bake one sheet at a time until the buns are puffed and lightly golden, about 10 minutes for the smaller buns and slightly longer for the larger. Reduce the heat to 350 degrees and continue to bake until the buns have dried out and the insides are set, about 10 to 15 minutes. (Increase the heat back to 425 degrees and bake the second sheet in the same manner.) Cool the buns and set aside.
Step 1In a medium saucepan, combine the milk with the vanilla seeds and pod and bring to a simmer. Remove from heat.
Step 2While the milk is heating, in a medium bowl, whisk the egg yolks with the sugar and cornstarch. When the milk has come to a simmer, whisk a small amount of milk in with the egg mixture to temper the eggs, then pour the egg mixture in the saucepan with the milk. Return the pan to medium heat and cook, stirring constantly and scraping the bottom of the pan, until the mixture has thickened to form a thick custard. Remove from heat and strain into a medium bowl.
Step 3Immediately stir in the butter and raspberry puree, then cool the mixture by placing the bowl over a larger bowl of ice water and stirring until the custard is chilled. This makes about 2 1/2 cups pastry cream.
Step 4Cover the surface of the custard with plastic wrap and refrigerate until needed.
Step 1In a bowl, combine the water and corn syrup. Place the powdered sugar in a large, heavy-bottom saucepan. Add the water and corn syrup mixture to the sugar and stir until well mixed. Place over low heat until melted (but don't allow the temperature to exceed 100 degrees).
Step 2Remove from heat and stir in the almond extract and the food coloring. This makes 1 1/4 cups fondant. It should be warm when coating the choux buns.
Step 1Fit a large pastry bag with a small tip suitable for piping a filling. Fill the bag with the chilled pastry cream.
Step 2Pierce a small hole in the bottom of the choux buns and fill each of the buns with the pastry cream until you can feel the weight of the cream inside. Set the filled buns aside.
Step 3Coat the tops of the buns by dipping them in warm fondant, shaking off the excess. Hold the buns upside down for a minute to give the fondant a chance to set, then gently invert and allow the fondant to dry. While the fondant is still a little tacky, assemble the religieuse by placing a smaller bun on top of a larger. Allow the fondant to dry completely.
Step 4Garnish with fresh raspberries.