Preheat the oven to 350°F (175°C). Place the unbaked pie crust in a 9-inch pie plate and crimp the edges; chill in the freezer for 10 minutes while preparing the filling.
In a medium microwave-safe bowl, combine the cubed butter and chopped bittersweet chocolate. Heat in 30-second intervals, stirring in between, until completely melted and smooth. Set aside to cool slightly.
In a large mixing bowl, whisk together the granulated sugar, brown sugar, and eggs until the mixture is light, aerated, and slightly pale (about 2 to 3 minutes).
Stir the vanilla extract and the cooled melted chocolate mixture into the egg and sugar mixture until fully incorporated.
Sift the flour, cocoa powder, and salt over the wet ingredients. Use a rubber spatula to gently fold the dry ingredients into the batter until no streaks of flour remain.
Fold in 3/4 cup of the semi-sweet chocolate chips.
Pour the brownie batter into the chilled pie crust, spreading it evenly to the edges.
Sprinkle the remaining 1/4 cup of chocolate chips over the top of the batter.
Bake for 35 to 40 minutes, or until the edges of the brownie are set and the top has formed a thin, crackly crust, but the center still has a slight wobble when shaken gently.
Remove from the oven and cool on a wire rack for at least 45 minutes to allow the gooey center to set before slicing. Serve warm with vanilla ice cream if desired.