Make the pastry cream: in a medium saucepan, combine 1 cup milk and 1/2 cup heavy cream and heat over medium until just before simmering (small bubbles forming at the edge). Remove from heat and set aside.
In a medium bowl, whisk together 1/2 cup (100 g) granulated sugar, 2 tablespoons cornstarch, 1/4 teaspoon salt, and 4 large egg yolks until smooth and pale.
With the whisk running, slowly drizzle about one-quarter of the hot milk/cream into the egg-yolk mixture to temper the eggs, then continue dripping in the remaining hot milk/cream while whisking constantly until fully combined.
Pour the tempered egg mixture back into the same saucepan. Cook over medium heat, whisking constantly, until the mixture thickens, comes to a gentle boil, and reaches the consistency of thick pudding (about 3–6 minutes). Keep whisking vigorously until smooth.
Remove from heat and stir in 1 teaspoon vanilla extract. Immediately pour the pastry cream through a fine-mesh strainer into a medium bowl, using the whisk or a spatula to push it through to remove any cooked bits.
Press a piece of plastic wrap directly onto the surface of the pastry cream to prevent a skin, then refrigerate until completely chilled, at least 1 hour.
Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper or a silicone baking mat.
Make the choux dough: in a medium saucepan, combine 1/2 cup water, 1/4 cup (2 oz) diced unsalted butter, 1 teaspoon sugar, and 1/4 teaspoon salt. Bring to a rolling boil over medium-high heat, stirring occasionally.
As soon as the butter is melted and the mixture is boiling, add 1/2 cup (60 g) all-purpose flour all at once. Stir vigorously with a wooden spoon until the flour is fully incorporated and the dough pulls away from the sides and forms a thin film on the bottom of the pan.
Transfer the dough to a large bowl and let it cool for about 4 minutes, until it is no longer hot to the touch.
Add 2 to 3 drops red food coloring to the cooled dough, then add the first of the 2 large eggs. Stir with the wooden spoon until the egg and coloring are fully incorporated and the dough is smooth. Add the second egg and stir until the dough is glossy and just holds its shape when lifted.
Transfer the dough to a pastry bag fitted with a 5/8-inch tip. Pipe mounds about 1 1/2 inches in diameter on the prepared baking sheet, leaving about 1 inch between each mound. If any peaks form, wet your fingertip and gently smooth them to prevent burning.
In a small bowl, whisk together 1 large egg and 1 tablespoon water to make the egg wash. Gently brush the tops of each piped puff with the egg wash.
Bake in the preheated oven for 25 minutes without opening the oven door. After 25 minutes, check the puffs: they should be lightly browned. If they are not, bake an additional 2–5 minutes until lightly golden. Remove from the oven and cool completely on a wire rack before filling.
To fill: poke a small hole in the bottom or side of each cooled cream puff with a chopstick or small sharp knife. If the pastry cream has firmed too much in the fridge, whisk it for about 30 seconds until smooth and pipeable.
Transfer the chilled pastry cream to a piping bag fitted with a 1/8-inch round tip and fill each cream puff through the hole until generously filled.
Serve immediately or keep filled cream puffs refrigerated until serving.