Combine 1 cup water, 1/2 cup cubed unsalted butter, and 3/4 teaspoon kosher salt in a medium, heavy-bottomed saucepan. Cook over medium-low heat, stirring frequently, to melt the butter. Once the butter has melted, increase the heat to medium-high and bring to a simmer. Remove the pan from heat and immediately stir in 1 1/4 cups all-purpose flour and 2 tablespoons plus 2 teaspoons granulated sugar with a wooden spoon. Continue to stir for about 2 minutes (or until the mixture has a paste-like consistency), then place over medium heat and stir rapidly for 1 to 2 minutes, or until the dough pulls away from the sides of the pan and the bottom of the pan is clean. The dough should be glossy and smooth, but not dry.
Immediately transfer the dough to the bowl of a stand mixer fitted with a paddle attachment. Beat on low for 30 seconds to release some of the moisture. With the mixer on low, slowly add 1 cup whisked eggs, 3 tablespoons at a time, beating until each addition is completely absorbed before adding the next addition. After all the eggs are added, the dough should come away from the sides of the bowl when pulled with the paddle, but then grab back on again. Increase the mixer to medium and mix for 15 seconds to make sure all the eggs are incorporated.
Scape the dough into a pastry bag fitted with an open star tip. Refrigerate until cool, about 1 hour. While the choux pastry is chilling, prepare your oven. Position a the racks in the upper and lower thirds of the oven and preheat to 375 (F). Line two sheet pans with parchment paper and set aside.
Once the dough is chilled, it's time to pipe the eclairs. Starting at the side of the parchment farthest away from you, hold the tip of the pastry bag 3/4 inch above the parchment and apply gentle, steady pressure as you pipe the first eclair. When the eclair is about 6 inches long, begin to lessen the pressure, and then stop it as you brng the dough back over itself, leaving a 1/2 inch curl at the end of the eclair. Pipe 5 more eclairs on the parchment, leaving about 2 inches between each eclair. Repeat with the second sheet pan, piping 6 more eclairs.
Wet the tip of your finger and press down the tip of each eclair, then spray them lightly with water. Place the sheet pans in the oven, placing one on the upper third and the second on the lower third, and immediately lower the oven temperature to 350 (F). Bake for 20 minutes, then switch the pans' positions, and bake for an additional 20 minutes. After 20 minutes, lower the oven to 325 (F) and bake for an additional 20 minutes, or until golden brown. Lower the temperature to 300 (F) one last time and bake for 10 minutes longer, or until the puffs are light and hollow (tap the bottom of an eclair to test this).
Set the pans on a wire rack and allow the eclairs to cool completely on the sheet pans before filling and glazing.