Make the cream puffs: Preheat the oven to 400º. In a medium saucepan, combine the water, sugar, salt and butter. Bring to a simmer over medium-high heat. Once simmering, reduce the heat to medium and add the flour. Using a wooden spoon, stir the mixture constantly until thickened and a thin film forms on the bottom of the pan, 4 to 5 minutes.
Transfer this mixture to the bowl of a stand mixer fitted with the paddle attachment and mix for 2 minutes to slightly cool down the dough. One at a time, add the eggs, making sure each one is completely incorporated before adding the next. Transfer the pâte à choux batter to a piping bag fitted with a ⅝-inch round tip (#808 tip).
Line 2 sheet pans with parchment paper and pipe 1-inch rounds of dough 1½ inches apart. The puffs will have a tail at the top where you piped them. Using a small bowl of water, dip your finger and smooth the tails for a perfectly round puff.
Bake for 10 minutes, then rotate the trays and reduce the temperature to 375º. Continue to bake until golden brown and puffed, another 20 minutes. Let cool completely, then puncture a small hole in the bottom of each puff using a ⅛-inch star tip or paring knife.
Make the spiced cream: In a large bowl, whisk all the ingredients together to stiff peaks. Transfer to a piping bag fitted with a ⅛-inch round tip. Fill each puff with spiced cream.
Glaze and decorate the cream puffs: Place the white chocolate chips in a medium glass bowl. In a microwavable bowl, microwave the corn syrup on high until syrupy in viscosity, 1 minute. Pour the syrup over the white chocolate chips and add the food coloring, then whisk until smooth. If there are any lumps of chocolate remaining, microwave in 20-second intervals until the mixture is smooth.
Begin glazing the cream puffs by dipping the top third into the glaze and scraping off any excess. Garnish with sprinkles while the glaze is wet, then let cool to set. As the glaze cools it will become more viscous; feel free to reheat it in the microwave or switch to spreading the glaze with an offset spatula. Once all of the cream puffs are glazed and decorated, place them somewhere cool to keep the glaze firm.
Make the caramel: In a medium saucepan fitted with a candy thermometer, combine the sugar and water over high heat. Cook, stirring constantly until the sugar has dissolved, 2 minutes. Once the mixture begins to simmer, cook, without stirring, until it reaches 310º, 8 minutes more. Remove from the heat and set next to your croquembouche cone and the cream puffs.
Begin dipping the bottom of each cream puff and sticking it to the cone, using the sugar as glue. Continue this process, working from the bottom up, until all the cream puffs are attached to the cone. Dip a fork in the hot sugar, then pull it up and begin spinning it around the cone, forming threads of sugar. You have to work fast, since the sugar cools quickly. Continue this process of pulling sugar until the whole cone is wrapped.
Place a sugar cookie star at the top of the tree, then serve.