Preheat the oven to 350 degrees F. Butter the bottom and side of a 91/2-inch deep-dish pie plate. Make the brownie filling: Heat the butter, chocolate chips and brown sugar in a medium saucepan over medium heat, whisking occasionally, until the butter and chocolate are melted. Remove from the heat. Whisk in the eggs, one at a time, then the vanilla, whisking until smooth. Whisk in the flour, cocoa powder, baking powder and salt until combined.
Pour about one-third of the brownie batter into the prepared pie plate; set aside the remaining batter. Bake until just starting to set and the top is shiny, about 20 minutes.
Meanwhile, make the pumpkin filling: Combine the pumpkin puree, heavy cream, egg, granulated sugar, flour, pumpkin pie spice and salt in a medium bowl; whisk until smooth.
Pour the pumpkin filling over the warm brownie layer. Stir 1 tablespoon water into the remaining brownie batter, then spoon the batter (in about 6 scoops) onto the pumpkin filling. Use the back of the spoon to pull the brownie batter into the pumpkin filling and create a swirled pattern. Bake until the pie is set, 40 to 45 minutes. Transfer to a rack and let cool completely. Serve with vanilla ice cream.