Preheat the oven to 425˚F (220˚C). Arrange racks in lower and upper thirds of the oven. Line 2 baking sheets with parchment papers.
In a medium bowl, add 3 eggs and whisk together. In another small bowl, add 1 egg and whisk together. Set both aside.
In a medium saucepan, combine butter, water and salt. Bring to just a rolling boil over high heat, stirring occasionally to melt the butter. Remove from heat. Add the flour all at once, stirring vigorously with a flexible spatula. Return to the stove and cook over medium heat. Stir and mash the dough until it comes together and leaves a film on the bottom of the pan. Continue to stir and cook for another 3 minutes.
Transfer the dough to an electric mixer fitted with a paddle attachment, beat on medium-low speed for 2 minutes to cool slightly. Add the beaten eggs in 4 additions. After each addition, the dough will look curdled at first, then it will form back into a soft dough. Scrap down the sides of the bowl after each addition.
Check the dough. When it’s ready, the dough should be smooth and pipe-able. When dip the paddle attachment in the dough, some dough will slide back and some should leave behind a “V” shape on the paddle. If the dough is too thick, add half or whole 4th egg if needed.
Fit a pipping bag with a ½-inch tip and fill the bag with dough. Pipe 14 (3½ x ¾ inches) logs. Repeat with the other baking sheet. To smooth out the sharp tops, push down slightly with a clean and wet finger.
In a small bowl, whisk together a large egg yolk and 1 tablespoon water. Brush the top and the side of the dough with egg wash. Gently drag a fork along the top of the logs the long way to make slight indentations (for even expansion).
Transfer to oven and bake for 12 – 15 minutes until they look puffed. Rotate the baking sheets from top to bottom and front to back for even baking. Lower the oven to 375˚F (190˚C). Bake for another 18 – 20 minutes until the eclairs feel firm when gently squeezed and sound hollow when tapped on the bottom, rotating the baking sheets once again after 12 minutes. Once again, lower the oven to 300˚F (150˚C). Bake for 15 more minutes, rotating the baking sheet half way through.
Transfer the shells to cooking rack and cool completely.
For the whipped cream, in a large mixing bowl with an electric mixer fitted with a whisk attachment, add cold heavy cream, sugar and vanilla. Beat over high speed until stiff peaks form. Transfer to a pipping bag fitted with a large star tip.
To assemble, cut the shells in half lengthwise. Pipe the whipped cream inside the bottom half of each shell. Carefully top 3 mango cubes on top of the whipped cream on each shell. Pipe 3 small dots of whipped cream on top of each mango cubes (to keep the top shell in place). Put the top shell back on the éclair. Transfer the eclairs to a large plate or baking sheet. Keep in the fridge.
Meanwhile, make the chocolate glaze. In a medium heatproof bowl, add the chocolate and butter. Set the bowl over a pot of simmering water. Stir to melt slightly.
In a small heatproof bowl, combine heavy cream and salt. Heat in the microwave until warm. Pour the cream over the chocolate. Stir until the chocolate is completely melted. Stir in corn syrup until the glaze is smooth and shiny. Set aside.
For the mango glaze. Puree the mango flesh in a blender or food processor until smooth. Measure out 4 tablespoons to use. In a medium bowl, add the powdered sugar and 3 tablespoons puree. Whisk until smooth. Add more puree if the glaze is too thick.
Take the eclairs out of the fridge. Spoon the glaze over the eclairs. Use the back of the spoon to smooth out the top. Return the eclairs to the fridge for 15 minutes to set. Serve within 6 hours.