Preheat oven to 425 degrees F. Line a baking sheet with parchment paper.
Combine butter with water and salt in a heavy saucepan. Heat over high heat and bring to a rolling boil. Reduce heat to low and add flour. Beat with a wooden spoon until the dough comes together. Remove from heat and add the eggs one at a time, fully incorporating each egg before adding the next.
Drop dough by heaping tablespoons onto the prepared baking sheet or pipe dough using piping bag. Bake for 20 minutes then lower the oven temperature to 350 degrees F. Continue to bake for another 10 minutes or until golden brown. The shells should sound hollow when done. Cool the shells completely on a wire rack.
Meanwhile, prepare the filling. Heat milk in a heavy saucepan over medium heat until warm.
Whisk together yolks and egg with pumpkin puree, cinnamon, sugar, cornstarch and salt. Slowly pour hot milk into yolk mixture, whisking constantly. Transfer mixture to saucepan and heat over low heat, stirring constantly. Cook until thick, about 6-7 minutes. Remove from heat and add the butter and vanilla. Strain the custard through a fine mesh sieve and cover with plastic wrap directly touching the surface. Let cool completely, about 1 hour.
Cut tops of the shells. Fill each cream puff with pumpkin custard. Dust with powdered sugar and serve.
Notes
The pumpkin custard and profiteroles can be prepared the day before. Wait to fill the cream puffs until ready to serve.