Set an oven rack in the middle. Place a rimmed baking sheet on the rack and preheat the oven to 350°F. Spread walnuts on a separate pan and toast for 6–8 minutes, until fragrant; cool slightly.
In a large bowl, whisk the eggs with the brown sugar for 1–2 minutes until glossy and slightly thickened.
In a small saucepan over low heat (or in a microwave-safe cup), warm the maple syrup with the melted butter just until fluid and warm to the touch, 1–2 minutes. Let stand 1 minute, then slowly stream into the egg mixture while whisking constantly to temper.
Whisk in vanilla, bourbon, flour, cinnamon, espresso powder, and fine sea salt until no dry spots remain. Fold in the toasted walnuts and chocolate chips.
Set the unbaked pie shell on the preheated baking sheet. Pour in the filling and smooth the top. Bake at 350°F for 40–45 minutes, rotating once halfway through. If the crust edges darken early, shield them loosely with foil. The pie is done when the outer ring is set and the very center has a slight wobble.
Transfer to a rack and immediately sprinkle the surface with flaky sea salt. Cool completely, at least 2 hours, before slicing so the custard firms and the chocolate sets.