Preheat oven to 375°F (190°C). Line 2 to 3 baking sheets with parchment paper.

Using a permanent marker and a 1½-inch round cutter as a guide, draw circles at least 1½ inches apart on another sheet of parchment paper; slide template under parchment on a prepared pan.

In a medium saucepan, bring butter, ⅓ cup (80 grams) water, milk, granulated sugar, and salt to a rolling boil over medium-high heat. Using a wooden spoon, stir in flour. Cook, stirring constantly, until a skin forms on bottom of pan and mixture pulls away from sides of pan and forms a ball, 1 to 2 minutes.

Transfer mixture to the bowl of a stand mixer fitted with the paddle attachment; beat at medium speed until dough cools slightly, 3 to 4 minutes. Add 3 eggs (150 grams), one at a time, beating until combined after each addition. Batter will be shiny and will slowly move back together when a spatula is dragged through it.

Transfer batter to a large pastry bag fitted with a ½-inch round piping tip (Ateco #805). Place piping tip in center of a drawn circle. Holding tip perpendicularly ½ inch above parchment paper and stationary the entire time, apply even pressure until batter reaches edges of drawn circle. Stop applying pressure, and move tip in a quick circular motion as you lift away to help prevent a point from forming on top. Repeat with remaining batter until pan is full. Wet your finger with water, and press down any points to create a smooth top, if necessary. Slide template out from under piped batter, and place under parchment on other prepared pans; pipe remaining batter.

In a small bowl, beat remaining 1 egg (50 grams). Using a pastry brush, brush egg onto piped dough; sprinkle with pearl sugar.

Bake, one pan at a time, for 10 minutes. Rotate pan, and bake until fully puffed and deep golden brown, about 10 minutes more. Let cool completely on pans. Serve immediately.