Preheat the oven to 350°F (175°C).
In a large mixing bowl, whisk together the melted butter and granulated sugar until the mixture is well combined and slightly pale.
Add the eggs one at a time, whisking thoroughly after each addition until the batter is smooth.
Stir in the vanilla extract.
Gently fold in the sifted flour, cocoa powder, and salt using a rubber spatula until just combined; do not overmix.
Pour the chocolate batter into the unbaked pie shell, smoothing the top with a spatula.
Bake for 30 to 35 minutes, or until the edges are set and the top has formed a thin, papery crust, while the center remains slightly soft to the touch.
Remove from the oven and allow to cool on a wire rack for at least 20 minutes to set before slicing.
Serve warm with a scoop of vanilla bean ice cream or a dollop of whipped cream.