In a saucepan, combine butter, water, sugar, and salt. Bring to a boil, then add flour all at once. Stir until the mixture forms a ball and pulls away from the sides. Remove from heat, let cool slightly, then add eggs one at a time, mixing well after each addition. Pipe the dough into circular shapes onto a baking sheet.

Bake

Preheat the oven to 400°F (200°C). Bake for about 25-30 minutes until golden and puffed. Let cool completely.

Making the Pistachio Mousseline Cream

Prepare the Custard

In a saucepan, heat milk and sugar. In a bowl, whisk egg yolks, then pour the hot milk over them, whisking constantly. Return to the saucepan and cook until thickened. Dissolve gelatin in water and mix into the custard. Cool to room temperature.

Combine with Butter and Pistachio

Beat butter until creamy, then gradually add the cooled custard and pistachio paste, mixing until smooth.

Making the Chocolate Glaze

Melt the Chocolate

In a microwave or double boiler, heat the chocolate and cream together until melted and smooth. Let cool slightly before using.

Preparing Passion Fruit Coulis

Combine Ingredients

In a saucepan, combine passion fruit puree, sugar, and lemon juice. Heat gently until the sugar dissolves. Cool before serving.

Making Mango Sorbet

Blend and Freeze

Blend mango puree, sugar, and lemon juice until smooth. Pour into an ice cream maker and churn according to the manufacturer's instructions. Freeze until firm.

Assembling the Paris-Brest

Fill and Decorate

Slice the cooled choux pastry in half, fill with pistachio mousseline cream, and drizzle with chocolate glaze. Serve with passion fruit coulis and a scoop of mango sorbet on the side.