Preheat the oven to 400° and position racks in the upper and lower thirds of the oven. Line 2 baking sheets with parchment paper. In a medium saucepan, combine the milk, water, butter, sugar and salt and bring to a boil. Remove from the heat, add the flour all at once and stir until incorporated. Cook the choux pastry over moderately low heat, stirring vigorously, until the dough comes together in a cohesive mass, about 2 minutes.
Scrape the dough into a standing electric mixer fitted with the paddle. At medium speed, beat in 1 egg until fully incorporated. Beat in the remaining eggs, 1 at a time.
Scrape half of the dough into a large pastry bag fitted with a 1/2-inch plain tip. Pipe 20 mounds, about 1 1/4 inches wide, onto 1 of the prepared baking sheets, about 1 inch apart. With lightly moistened fingers, press down any peaks. Fill the pastry bag with the remaining dough and pipe twelve 5-by-3/4-inch eclairs onto the second sheet. Bake the puffs and eclairs for about 25 minutes, until golden and risen, shifting the pans from top to bottom and front to back halfway through baking. Let cool completely on the pans. Using a sharp knife, poke holes in the sides of the pastries for filling.
In a medium saucepan, heat the milk just until small bubbles appear around the edge. Add the vanilla bean, cover and let stand off the heat for 10 minutes. Discard the vanilla bean.
In a small bowl, whisk the egg with the granulated sugar and cornstarch. Gradually whisk in the warm milk. Transfer the mixture to the saucepan and cook over moderate heat, whisking vigorously, until very thick, smooth and shiny, 3 to 4 minutes. Scrape into a bowl and let cool slightly. Whisk in the butter. Press a sheet of plastic wrap directly onto the surface of the pastry cream and refrigerate until chilled, about 2 hours.
In a medium bowl, beat the heavy cream until firm peaks form. Fold the whipped cream into the pastry cream along with the pistachios. Transfer half to a pastry bag fitted with a 1/4-inch plain tip. Poke the tip into the eclairs and puffs and fill them with pastry cream. Return them to the baking sheets.
In a medium bowl, using a handheld electric mixer, beat all of the ingredients together until a thick, pourable glaze forms. Dip the tops of the puffs and eclairs in the glaze and return to the sheets to set, about 10 minutes.
The filled and glazed eclairs and cream puffs can be refrigerated in an airtight container for up to 8 hours.