Preheat the oven to 400 degrees F (200 degrees C). Line 2 baking sheets with parchment paper.
Combine water, butter, and salt for pastries in a saucepan on the stove; bring to a brisk boil. Add flour, then turn off the heat and stir vigorously until mixture is smooth.
Pour mixture into a large mixing bowl. Beat in eggs, one at a time, until mixture is thick and shiny. Spoon 12 dollops of the mixture onto each of the prepared baking sheets, about 2 inches apart.
Bake in the preheated oven until light golden brown, about 30 minutes, swapping racks halfway through. Remove to cooling racks and let cool, about 30 minutes.
Meanwhile, combine milk, condensed milk, sugar, eggs, and salt for filling in a pot over medium-high heat. When the mixture starts to steam, reduce heat to medium.
Place cornstarch in a bowl and stir in about 2 tablespoons of the hot milk mixture. Stir vigorously until it's completely liquid, then pour into the pot with the remaining milk mixture. Cook, stirring constantly, until custard thickens.
Turn off the heat, add vanilla, and continue stirring for about 8 minutes. Let cool, about 10 minutes; it will thicken as it cools.
Cut the tops off the cooled pastries. Add the custard filling and put the tops back on. Place in the refrigerator for 1 hour before serving.