Preheat oven to 350°F. Place prepared pie shell onto a sheet tray. If you like your crust more golden, see step 2. If not, skip to step 3.
Prebake Crust: Place a square of parchment paper into the center of your prepared pie shell. Top the parchment with pie weights or dried beans, making sure to cover the entire interior surface. Bake for 15 minutes. Remove from oven. Carefully lift out the parchment and weights. Prick little holes into the bottom of the pie dough with a fork. Place back into the oven to bake for about 5 minutes. Set aside.
For the Chocolate Filling: Melt the butter and semi-sweet chocolate together in a microwave-safe bowl. Whisk to completely combine and emulsify. Transfer chocolate-butter mixture to a large bowl, or the bowl of a standing mixer. *If using a standing mixer, be sure to use the whisk attachment.
In a medium-sized bowl, whisk together the sugar, flour, cocoa powder, instant espresso, and salt. Pour dry ingredients into the chocolate-butter mixture and whisk until combined. Add the vanilla, stir to combine. Add the eggs, one at a time, mixing until smooth and combined. Pour the batter into the prepared pie shell.
Bake the pie until the filling is puffed and set in the center, about 30 to 35 minutes. The filling should still be slightly jiggly, be careful not to over-bake. Allow pie to cool and completely set before slicing. Serve warm or at room temperature, with whipped cream or vanilla ice cream.
The pie can be kept at room temperature, covered, for up to 3 days. Or stored in the refrigerator, covered, for up to 5 days.