Special equipment: 1 piping bag fitted with a large round tip and 2 piping bags fitted with medium round tips; a sugar wand or whisk
For the pate a choux: Preheat the oven to 425 degrees F. Line 3 baking sheets with parchment.
Bring the milk and butter to a boil in a medium saucepan over medium-high heat. Add the flour, reduce the heat to low and cook, stirring, until a carpet, or thick film, forms on the bottom of the pan. Add the mixture to a stand mixer fitted with a paddle attachment while still hot. Turn to medium speed and beat, adding one egg at a time, until fully combined and glossy.
Transfer the mixture to a piping bag fitted with a large round tip. Pipe 2-inch balls spaced about 2 inches apart on the prepared baking sheets (you should have about 55 balls). Bake until golden brown, about 22 minutes. Reduce the heat to 350 degrees F and bake another 15 minutes to dry them out.
Let the puffs cool on the baking sheets for 5 minutes and then transfer to racks and let cool completely before filling, preferably overnight. Puncture small holes in the base of each puff and set aside to fill.
For the quince and prickly pear jam: Heat the quince paste, prickly pear juice and vanilla extract in a saucepan over low heat, stirring until fully combined. Let cool completely. Transfer the mixture to a piping bag fitted with a medium round tip. Pipe the jam into the pate a choux puffs through the holes in the bottoms, filling the puffs halfway.
For the vanilla bean whipped cream: Beat the cream and vanilla paste together in a stand mixer fitted with a whisk attachment until beginning to thicken. Slowly add the sugar and beat just until stiff. Then stop!
Transfer the cream to a piping bag fitted with a medium tip. Pipe the cream into the pate a choux puffs.
For the treacle maple syrup: Combine the treacle, maple syrup and vanilla bean paste in a small saucepan and bring to a boil over medium heat. Let cool halfway so it is still liquid.
To assemble the croquembouche: Dip each filled pate a choux puff into the treacle syrup and stack on a serving tray to build a tower. Let set, 20 to 30 minutes.
For the crisp caramel sugar: Heat the sugar in a small saucepan over medium heat, making sure not to stir. Cook until melted and golden brown. Allow to cool halfway.
Dip a sugar wand or whisk into the caramel and quickly wave it in circles around the tower to create caramel strands. Repeat to create a wispy caramel cage. Serve immediately.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.