How to Make It
In a large saucepan, combine the milk, sugar, vanilla bean and seeds and bring to a boil. Simmer over moderate heat for about 1 hour and 40 minutes, stirring frequently, until the milk jam is golden and the consistency of sour cream; the milk jam may break and separate. Discard the vanilla bean. Transfer the milk jam to a blender or food processor and process until smooth and creamy, about 1 minute. Transfer the milk jam to a heatproof container and refrigerate.
Meanwhile, preheat the oven to 400°. Line 2 large baking sheets with parchment paper. Position racks in the middle and lower third of the oven. In a medium saucepan, bring the water to a boil. Add the butter and salt and cook over moderate heat just until the butter is melted. Add the flour all at once and stir vigorously with a wooden spoon until the dough comes together in a cohesive mass, 1 to 2 minutes. Remove from the heat and let stand for 2 minutes. Using a handheld electric mixer, beat the dough at medium speed for 1 minute. Beat in 1 egg at a time until a sticky dough forms.
Transfer the dough to a large pastry bag fitted with a 1-inch plain tip. On each baking sheet, pipe out eight 6-by-1-inch ropes. Using a moistened finger tip, smooth out any points or spikes of dough. Bake the éclairs for 25 minutes, until lightly golden and risen, shifting the pans from top to bottom and front to back halfway through.
Reduce the oven temperature to 250° and bake for 20 minutes longer, until the éclairs are crisp and golden. Carefully poke both ends of each éclair with a skewer to allow steam to escape. Turn the oven off and let the éclairs sit with the door slightly ajar for 30 minutes, until the insides are somewhat dry. Remove from the oven and let cool completely.
In a large bowl, using an electric mixer, beat the heavy cream at high speed until firm. Transfer 3/4 cup of the milk jam to a medium bowl and beat in one fourth of the whipped cream. Fold the milk jam mixture into the remaining whipped cream until no streaks remain. Fill a pastry bag fitted with a 1/4-inch plain tip with half of the milk jam cream. Squeeze the cream into both ends of each éclair to fill. Alternatively, split each éclair horizontally, spoon the filling in and replace the tops. Transfer the éclairs to a platter.
Spoon about 1/2 cup of the milk jam into a microwave-safe bowl and heat until spreadable, about 20 seconds. Spread about 1 1/2 teaspoons of the milk jam on top of each éclair and serve.