Preheat oven to 425°F. Line two lightly colored 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. Heat over medium 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 until the flour is fully incorporated.
Return the pan to medium heat and cook, stirring constantly, until the mixture smooths out and pulls away from the sides of the pan and follows the spoon (about 30 seconds). Remove from heat and let cool 5–10 minutes, until warm but not hot.
Transfer the dough to a bowl or the bowl of a stand mixer. Beat in 4 large eggs one at a time, fully incorporating each egg before adding the next. After the last egg, beat for at least 2 minutes until the batter is smooth and glossy.
Using a generously filled tablespoon scoop, drop 3– to 4-tablespoon mounds of batter onto the prepared baking sheets, spacing mounds about 3 inches apart.
Bake at 425°F for 15 minutes. Without opening the oven door, reduce the temperature to 350°F and bake an additional 25 minutes, until the pastries are a medium golden brown.
Remove the baking sheets from the oven. Make a small slit in the top of each puff and return the sheets to the oven for 5 minutes to allow steam to escape and dry the interiors. Transfer puffs to a rack to cool.
When cool enough to handle, split each puff in half horizontally to make top and bottom pieces.
To make the lemon filling: in a medium bowl, whisk the 3.4 oz box instant lemon pudding with 1 cup milk until smooth and slightly thickened.
In a separate chilled bowl, whip 1 1/2 cups heavy cream with 2 tablespoons sugar and 1 teaspoon vanilla until soft-to-medium peaks form.
Gently fold the pudding mixture into the whipped cream until uniform. Stir in the zest of 1 lemon.
Fill each cream puff bottom generously with the lemon cream, replace the tops, and dust with powdered sugar. Refrigerate filled cream puffs until ready to serve.