Preheat oven to 375°F (190°C). Using a permanent marker and a 2-inch round cutter as a guide, draw 30 circles onto 2 sheets of parchment paper. Turn parchment over, and place on 2 baking sheets.

In a medium saucepan, melt butter over medium heat. Add ½ cup (120 grams) water, milk, granulated sugar, and salt; bring to a boil. Using a wooden spoon, stir in flour. Cook, stirring constantly, until a skin forms on bottom of pan, 1 to 2 minutes. Transfer mixture to the bowl of a stand mixer fitted with the paddle attachment. With mixer on low speed, beat until dough is warm to the touch, about 1 minute. Add eggs and egg white, one at a time, beating until combined.

Transfer batter to an 18-inch piping bag fitted with a ½-inch round tip*. Place piping tip in center of one drawn circle. Hold tip perpendicular ½ inch above parchment paper. Holding tip stationary the entire time, apply even pressure until batter reaches edges of drawn circle. Stop applying pressure, and lift up. Wet your finger with water, and press down tip to create a smooth top. Repeat with remaining batter.

Bake for 15 minutes. Rotate pans, and bake until fully puffed and deep golden brown, about 10 minutes more. Let cool completely on wire racks.

Using a ¼-inch round piping tip, poke a hole in center of bottom of each puff. Insert a skewer into hole, and move it around to ensure cream will fill entire puff. Fill a pastry bag fitted with same tip with Vanilla Crème Mousseline. Place piping tip into hole, and apply gentle pressure to fill. Repeat with remaining puffs and Vanilla Crème Mousseline. Dust with confectioners’ sugar, if desired. Serve immediately, or refrigerate until ready to serve. Best served same day.

In a large saucepan, whisk together milk, ½ cup (100 grams) sugar, and vanilla bean and reserved seeds. Heat over medium heat until steaming. Discard vanilla bean.

In a large bowl, whisk together egg yolks, cornstarch, salt, and remaining ½ cup (100 grams) sugar. Gradually add warm milk mixture to egg mixture, whisking constantly. Pour mixture back into saucepan, and cook over medium heat, whisking constantly, until thickened and boiling, 4 to 5 minutes. Strain mixture through a fine-mesh sieve into a large bowl. Stir in softened butter in two additions. Cover with a piece of plastic wrap, pressing wrap directly onto surface of pastry cream to prevent a skin from forming. Refrigerate until an instant-read thermometer registers 65°F (18°C) to 70°F (21°C), 2½ to 3 hours.

In the bowl of a stand mixer fitted with the paddle attachment, beat room temperature butter at medium speed until smooth, about 1 minute. Remove pastry cream from refrigerator, and whisk to smooth. (At this point, butter and pastry cream should be same temperature.) With mixer on low speed, slowly add pastry cream to butter, letting each addition fully incorporate before adding the next, stopping to scrape sides of bowl as needed. Use immediately.