For the Pastry Cream
1. Heat the milk with the scraped seeds of the vanilla bean or the vanilla bean paste until just below a simmer.
2. In a separate bowl, whisk the egg yolks, sugar and cornstarch. Ready a bowl with the butter, placing a strainer on top of it.
3. Gradually whisk the hot milk into egg mixture and then return it all to the pot. Whisk this constantly (switching to a spatula now and again, to get into the corners) over medium heat until thickened and glossy, (just to a bubble,) about 2 minutes. Pour this immediately through the strainer, whisking it through if needed, and stir in the butter. Place a piece of plastic wrap directly over the surface of the custard, cool to room temperature and then chill completely until ready to use.
For the Choux Paste
1. Bring the milk, water, butter, sugar and salt up to a full simmer over medium high heat. Reduce the heat to low and stir in the flour with a wooden spoon, stirring vigorously until the dough “cleans” the sides of the pot (no longer sticks). Scrape this mixture into a large bowl and use electric beaters or a stand mixer fitted with the paddle attachment and beat on medium speed for a minute or 2 to cool it a little.
2. Break two eggs into a small dish and whisk them just to blend a little. Add these to the flour mixture while still on medium speed and mix until blended. Add the remaining 3 eggs one at a time and mixing well after each addition.
3. Work with this recipe while the batter is still warm.
For the Profiteroles
1. Make 2 recipes of choux paste.
2. For the profiteroles, preheat the oven to 400 F and line four baking trays with parchment paper.
3. Fill a piping bag fitted with a large plain tip with the choux paste. Pipe profiteroles, each about 1 1/2-inches across. Wet your finger in cool water and tap any points on the batter. It is alright for the piped profiteroles to sit out if you have to bake in batches.
4. Bake the profiteroles for 10 minutes, then reduce the heat to 375 F and continue to bake for about 15 more minutes, until they are a rich golden brown colour and are very light. Allow the pastries to cool completely before filling.
For the Assembly
1. Cover a 12-inch Styrofoam cone with parchment paper (the cone can be found at any craft store) and place this on a parchment lined baking tray.
2. Bring the water, sugar and corn syrup up to a boil in a small pot over high heat and continue to boil, uncovered and without stirring, and occasionally brushing the sides of the pot with water, until it is a light amber colour. Ready a bowl of ice water and carefully set the bottom of the pot into the ice water to halt the sugar from cooking further.
3. Using tongs carefully dip the bottoms of the profiteroles into the caramelized sugar and place them around the bottom of the cone, with the caramel bottom facing the cone, and so that they touch each other and the base of the cone. Continue dipping and arranging the profiteroles working upward until you have completely covered the cone. If the caramel in the pot begins to set before you have finished, you can reheat the caramel on low heat. If you wish, dip a fork in the caramel and carefully “spin” sugar around the outside. Let the sugar set for an hour, then carefully lift the croquembouche up, remove the cone and parchment and place the croquembouche onto a serving platter. Do not refrigerate.
4. The profiteroles themselves can be made and filled a day ahead and chilled, but the croquembouche must be assembled within 3 hours of being served.