Preheat the oven to 400°F (205°C). Line a baking sheet with parchment paper.
In a saucepan, combine milk, water, butter, sugar, and salt. Bring to a rolling boil.
Reduce heat to low and add flour all at once. Stir vigorously with a spatula until a smooth dough forms and pulls away from the sides.
Continue cooking the dough for 1–2 minutes to remove excess moisture.
Transfer dough to a mixing bowl and let cool for 5 minutes.
Add eggs one at a time, mixing fully after each addition. The dough should be thick, smooth, and pipeable.
Mix in vanilla.
Pipe or scoop large mounds (about 3 inches wide) onto the baking sheet, spacing well apart.
Bake at 400°F for 20 minutes, then reduce oven temperature to 350°F (175°C) and bake an additional 15–20 minutes until deeply golden and puffed.
Turn off the oven, crack the door, and let shells sit for 10 minutes before removing.
Cool completely on a rack.
In a saucepan, combine sugar and water. Do not stir.
Cook over medium-high heat until the sugar dissolves and the mixture turns amber, about 10–15 minutes.
Remove from heat immediately once a deep golden color forms.
Let cool slightly until thick but still pourable.