Preheat oven to 400 degrees F. Line a large baking sheet with parchment paper; set aside.
In a medium saucepan, combine water, butter, and 1/8 teaspoon salt. Bring to boiling. Add flour all at once, stirring vigorously. Cook and stir until mixture forms a ball that doesn't separate. Remove from heat. Cool for 10 minutes. Add 4 eggs, one at a time, beating well with a wooden spoon after each addition.
Drop 12 mounds of dough onto the prepared baking sheet. Using a moistened finger, smooth any rough peaks in the tops of the cream puffs.
Bake for 30 to 35 minutes or until golden brown and firm; cool. Cut tops from cream puffs; remove soft dough from insides.
Preheat oven to 325 degrees F. For pumpkin filling, in a heavy large saucepan, combine whipping cream, pumpkin, pumpkin pie spice, and 1/4 teaspoon salt. Bring to a simmer, whisking constantly. Remove from heat. In a medium bowl, combine 9 egg yolks and sugar. Whisk together until well combined. Slowly whisk 1/2 cup of hot cream mixture into egg yolk mixture, then whisk all of egg mixture into cream mixture. Pour custard through a fine-mesh sieve into a 2-quart square baking dish. Place the dish in a 13x9x2-inch baking pan. Add hot water to the baking pan to come half way up the sides of the baking dish. Bake for 50 to 60 minutes or until nearly set in the center when gently shaken. Cool. If desired, cover and chill until serving time.
Before serving, spoon filling into cream puffs. Replace tops. Spoon Chocolate Sauce atop profiteroles. Makes 12 profiteroles.
In a medium microwave-safe bowl, combine semisweet chocolate, water, butter, and sugar. Microwave on 100 percent power (high) for 1 minute or until chocolate is melted, stirring twice. Stir in vanilla.