Preheat the oven to 425°F (220°C). Line two baking sheets with parchment paper and set aside.
In a medium saucepan combine 1 cup water, 1/2 cup butter, and 1/4 teaspoon salt. Place over medium heat until the butter melts, then increase heat to high and bring to a rolling boil.
Remove the pan from the heat and add 1 1/4 cups all-purpose flour all at once. Stir vigorously with a wooden spoon or spatula until the flour is fully incorporated.
Return the pan to medium heat and cook, stirring constantly, until the dough smooths out and pulls away from the sides of the pan and follows the spoon (about 30 seconds). Remove from heat.
Let the dough cool for 5–10 minutes, until it is hot but not so hot that it would cook the eggs when added (you should be able to hold a fingertip in it briefly).
Transfer the dough to a mixing bowl or the bowl of a stand mixer. Add 4 large eggs one at a time, beating well after each addition. The dough may look curdled at times but should become smooth after the last egg. Beat for at least 2 minutes after the last egg to ensure the mixture is smooth and glossy.
Using a tablespoon-sized scoop or two spoons, drop generous mounds of the choux batter (about 3 to 4 tablespoons each) onto the prepared baking sheets, spacing them about 3 inches apart.
Bake at 425°F for 15 minutes. Without opening the oven door, reduce the oven temperature to 350°F (175°C) and continue baking for an additional 25 minutes, until the puffs are a medium golden brown.
Remove the baking sheets from the oven. Use a small knife to make a small slit in the top of each puff to release steam, then return the puffs to the oven for 5 minutes to dry the interiors. Transfer the puffs to a wire rack to cool.
While the shells cool, make the lemon filling: in a mixing bowl combine the 3.4 oz box of instant lemon pudding mix and 1 cup milk; then add 1 1/2 cups heavy cream. Beat the mixture with an electric mixer for 2–3 minutes, until light and fluffy.
Stir in 1 teaspoon vanilla, the zest of 1 lemon, and 2 tablespoons sugar into the filling until evenly combined.
When the cream puff shells are cool enough to handle, split each in half horizontally. Fill each bottom half generously with the lemon filling (spoon or pipe the filling), replace the tops, and dust with powdered sugar.
Refrigerate the filled cream puffs until ready to serve.