Prepare the Choux Pastry

1. Combine Ingredients: In a saucepan, combine water, milk, butter, salt, and sugar. Place over low heat until the butter is melted.
2. Boil: Once the butter is completely melted, turn the heat to high and bring to a boil.
3. Add Flour: As soon as it boils, remove from heat and add flour all at once. Mix well until the flour is absorbed.
4. Cook Dough: Return the saucepan to medium heat, cooking and stirring for 2-3 minutes until a layer of dough forms on the bottom of the pan.
5. Cool: Remove from heat and let the dough cool for 10 minutes.
6. Incorporate Eggs: Add the eggs one at a time, mixing well after each addition until the dough is smooth and forms a streak when you run your finger through it.
7. Pipe Dough: Spoon the dough into a pastry bag fitted with a round nozzle.

Prepare the Puff Pastry

8. Roll Puff Pastry: Roll out the sheet of puff pastry to a 0.5 cm thickness.
9. Cut and Pipe: Cut a 20 cm diameter circle and place it on a baking tray. Pipe a circle of choux pastry around the edge and pipe the remaining choux pastry into small dollops on a separate tray.
10. Bake: Bake at 350°F (180°C) for 35-40 minutes until golden brown and crisp. Allow to cool.

Vanilla Creme Diplomat

11. Bloom Gelatin: Bloom the gelatin in cold water.
12. Heat Milk: Heat milk in a pot over low heat.
13. Mix Yolks and Sugar: In a bowl, mix egg yolks, sugar, and salt until creamy.
14. Add Cornstarch: Mix in the cornstarch.
15. Cook Cream: Pour the hot milk into the egg mixture, then return to the pot and cook until thickened. Add gelatin and cool completely.
16. Mix Cream: Once chilled, mix with an electric mixer until smooth. Add vanilla, mascarpone, and fold in whipped cream.
17. Pipe Cream: Spoon into a pastry bag fitted with a St. Honore nozzle.

Caramel Creme Diplomat

18. Bloom Gelatin: Bloom the gelatin in cold water for at least 10 minutes.
19. Cook Caramel: Combine 80 g sugar with water in a saucepan over medium heat until it turns amber. Cool slightly, add milk, and heat until dissolved.
20. Mix Yolks and Sugar: Mix egg yolks, remaining sugar, and salt in a bowl. Add cornstarch and mix well.
21. Cook Cream: Pour the hot caramel milk into the egg mixture, return to heat, and cook until thickened. Add gelatin and cool.
22. Mix Cream: Once chilled, mix with an electric mixer until smooth. Fold in whipped cream.

Assemble the Gateau

23. Fill Choux Buns: Make a hole at the bottom of each choux bun and fill with caramel creme diplomat.
24. Caramelize Buns: Make a wet caramel with 150 g sugar and 65 ml water. Dip the tops of the filled buns and place on baking paper. Reheat caramel if it thickens and dip the bottom of each bun, gluing them to the puff pastry ring.
25. Fill and Decorate: Fill the bottom of the gateau with remaining caramel creme diplomat, then top with vanilla creme diplomat using the St. Honore nozzle. Decorate with choux buns and caramel strings before serving.