Combine the water, milk, butter, salt, and sugar in a saucepan, then warm it over low heat until the butter melts. Raise the heat and bring the mixture to a full boil. Remove from heat and add all the flour at once, stirring until absorbed. Return to medium heat and cook for 2 to 3 minutes, stirring constantly, until a thin film forms on the bottom. Let the dough cool for about 10 minutes.

Beat in the eggs one at a time until the dough is smooth and glossy. Use the last egg only if needed. Spoon the dough into a piping bag fitted with a round tip. Roll the puff pastry to about 1/4 inch thick and cut an 8-inch circle. Place on a baking tray, pipe a ring of choux around the edge, and pipe remaining choux into small mounds.

Bake at 350°F for 35 to 40 minutes, until the choux is golden and crisp. Cool completely. For the vanilla crèmer diplomat, sprinkle gelatin over cold water to bloom. Warm the milk over low heat, whisk yolks, sugar, and salt until creamy, then whisk in cornstarch. Pour the hot milk into the egg mixture, return to the pot, and cook until thick, stirring often. Stir in bloomed gelatin, then cool covered with plastic wrap.

Once the vanilla custard is cold, beat until smooth. Mix in vanilla and mascarpone, then fold in whipped cream. Next, bloom gelatin for caramel cream in cold water. Cook sugar with water over medium heat until amber. Add milk and warm until caramel dissolves. Whisk yolks, sugar, and salt, add cornstarch, pour in caramel milk, cook until thick, stir in gelatin, cool, beat smooth, and fold in whipped cream.

Poke a small hole in the bottom of each choux bun and pipe in the caramel crèmer diplomat. For wet caramel, cook sugar and water until amber. Dip tops of filled buns in caramel and place on baking paper. If caramel thickens, rewarm gently. Dip bottoms of each bun and press onto puff pastry ring. Fill center with remaining caramel cream, pipe vanilla cream on top with the St. Honoré tip, finish with caramel-glazed buns and a few caramel threads.

Serve the cake the same day for the crispiest caramel and best texture. If leftovers, cover and refrigerate up to 1 day. Note that the caramel will soften over time.