In a medium saucepan over medium-high heat, bring the 1 tablespoon butter, 1 teaspoon granulated sugar, 1 large pinch salt, and 3/4 cup water to a boil.
Add the 1 cup all-purpose flour and stir vigorously with a wooden spoon until the dough pulls away from the sides of the pan, gets hard to stir, and forms a stiff ball, 2 to 4 minutes.
Reduce the heat to medium and continue stirring (oof!) until a thin layer of dough films the bottom of the pan, 1 to 2 minutes.
Plop the dough in the bowl of a stand mixer fitted with the paddle attachment. Beat on low speed for 1 minute.
Add the 4 large eggs to the dough, 1 at a time, beating on medium-high speed after each addition until fully incorporated before adding the next, about 1 minute for the first egg and slightly less time for each subsequent egg, about 3 minutes total. The dough may release some steam and that's fine. When fully mixed, the batter will be glossy and smooth.
Cover the bowl with plastic wrap and refrigerate for 30 minutes.