Stir together 1 1/2 cups water, butter, granulated sugar, and salt in a medium saucepan. Bring to a simmer over medium-high, stirring occasionally. Add flour all at once, and stir vigorously with a wooden spoon until combined. Reduce heat to medium-low, and cook, stirring constantly, until a film develops on bottom of pan and dough pulls away from sides, 2 to 3 minutes. Transfer dough to bowl of a heavy-duty stand mixer fitted with the paddle attachment, and beat on medium-low speed until slightly cooled, about 2 minutes. Add eggs, one at a time, beating until mixture comes back together as a smooth dough after each addition. Press plastic wrap directly on surface of dough and chill at least 2 hours or up to 6 hours.
Preheat oven to 375°F. Transfer one-third of the dough to a large pastry bag fitted with a 1/2-inch round tip. Keep remaining dough in refrigerator. Pipe about 26 (1 1/4-inch) mounds 1 inch apart on a large parchment paper–lined baking sheet. (To help make a perfect circle, pipe mounds without moving the tip. Pipe as smoothly and evenly as possible, pulling tip quickly to 1 side when finished with each mound to prevent a Hershey’s Kiss look.) Using a wet finger, gently smooth any “beaks” on tops of mounds. Using a spray bottle filled with water, mist mounds, and place in preheated oven. Immediately reduce oven temperature to 350°F, and bake until golden brown and puffed, 35 to 40 minutes. Remove puffs from oven, and let stand on baking sheet until completely cool, about 30 minutes. Increase oven temperature to 375°F, and repeat process 2 times with remaining dough. (Make sure you use cool baking sheets each time.) Using a 1/3-inch round piping tip, poke a 1/4-inch-deep hole into bottom of each puff.