To prepare the hazelnut pastry cream, whisk together the milk, egg yolks, cornstarch, sugar, and vanilla paste in a medium saucepan. Place over medium heat and whisk constantly until the mixture thickens and bubbles. Remove from the heat and whisk in the butter and hazelnut paste until fully incorporated and smooth. Transfer the cream to an airtight container, press plastic wrap directly against the surface, and refrigerate until completely chilled.
For the choux pastry, combine the milk, water, butter, sugar, and salt in a medium saucepan and bring to a full boil over medium-high heat. Add all the flour at once, stirring vigorously with a wooden spoon until a smooth dough forms and pulls cleanly away from the sides of the pan, about 1–2 minutes. Transfer the dough to the bowl of a stand mixer fitted with the paddle attachment. Mix on low speed for 4 to 5 minutes to cool slightly. Gradually add the beaten eggs, mixing until the dough is smooth, glossy, and pipeable.
Preheat the oven to 340°F (170°C).
Transfer the dough to a piping bag fitted with a large star tip and pipe straight lines, each about 4.5 inches/11 cm long, onto a parchment-lined baking sheet. Dust lightly with powdered sugar. Bake for 35 minutes, or until puffed, golden brown, and firm to the touch. Cool completely on a wire rack.
For the ganache, heat the heavy cream in the microwave or in a small saucepan until just boiling. Place the chocolate in a heatproof bowl, pour the hot cream over it, and let sit for 1 minute. Add the salt, then whisk or blend with an immersion blender until smooth and glossy.
To assemble, use a piping bag fitted with a small round tip to fill each cooled éclair with hazelnut pastry cream. Dip the tops into the ganache, letting excess drip off, then smooth with your fingers if needed. Allow the glaze to set before serving, then shave dark chocolate on top.