Lightly grease a rimmed baking sheet and set aside. In a saucepan, combine water, sugar, corn syrup, hazelnuts, almonds, and salt. Cook over medium heat, stirring frequently, until mixture darkens to a tawny brown and registers 320°F (160°C).

Remove from heat and stir in baking soda, folding until foamy, then pour onto the prepared baking sheet. Let cool to room temperature.

Break praline into pieces and transfer to a food processor. Pulse several times to pulverize, then let run continuously until it becomes a thick paste.

Adjust oven rack to middle position and preheat oven to 375°F (190°C). Trace an 8-inch circle on a sheet of parchment paper and flip it over to set on a baking sheet.

Pipe choux pastry along the traced circle, applying steady pressure. Pipe a second ring inside the first, making sure they touch, and a third ring on top.

Smooth the surface of the dough with a wet finger. Brush with egg wash and sprinkle with sliced almonds.

Bake choux ring until puffed and golden brown, about 35 minutes. Turn off oven, partially open door, and let stand for 30 minutes. Remove from oven and let cool completely.

In a stand mixer, beat softened butter until fluffy, about 5 minutes. Add praline paste and beat until well combined.

With the mixer running, add pastry cream a few tablespoons at a time until incorporated. Switch to whisk attachment and whip until soft and airy.

Transfer cooled choux ring to a cutting board and cut in half horizontally. Pipe crème mousseline onto the bottom half and place the top half over it. Dust with powdered sugar and slice into portions.