How to Make It
Prepare the Puffs: Preheat oven to 425°F. Line 2 baking sheets with parchment paper. Combine butter, sugar, salt, and 1 cup of the water in a medium saucepan. Bring to a boil over medium-high, stirring occasionally. Reduce heat to medium-low, and add flour. Cook, stirring constantly, until mixture forms a ball and leaves a thin coating on the bottom of the saucepan, about 2 minutes. Transfer mixture to a bowl; let stand 10 minutes. Using an electric mixer, beat on medium speed, 2 minutes (mixture will look broken). Add whole eggs, 1 at a time, beating until dough is smooth and combined after each addition.
Using a piping bag or 2 spoons, scoop 22 golf ball-sized portions of dough onto prepared baking sheets. Whisk together egg yolk and remaining 1 teaspoon water in a small bowl. Lightly brush tops and sides of dough balls with egg mixture. Bake in preheated oven 15 minutes. Rotate baking sheets, top rack to bottom rack, and reduce oven temperature to 350°F. Bake until puffs are browned and crisp, 18 to 20 minutes. Remove from oven, and pierce bottoms of puffs with the tip of a knife to allow steam to escape. Cool completely on baking sheets, about 30 minutes.
Prepare the Pumpkin Cream: Whisk together brown sugar, granulated sugar, cornstarch, pumpkin pie spice, and salt in a small saucepan. Whisk in milk and egg yolks. Bring to a boil over medium, whisking constantly and cook, continuing to whisk constantly, until thickened, about 1 minute. Remove from heat. Stir in pumpkin, butter, and vanilla until butter melts and mixture is smooth. Transfer mixture to a bowl; cover with plastic wrap, placing plastic wrap directly on surface of cream to prevent a film from forming. Chill until cold, about 30 minutes.
Whip cream on high speed with an electric mixer until medium peaks form. Gently fold whipped cream into pumpkin mixture until just combined.
Split puffs in half and fill each with about 3 tablespoons pumpkin cream. Sift together powdered sugar and cinnamon and sprinkle evenly over tops of filled cream puffs.