Preheat oven to 350°F (175°C). Spread raw pecan halves across a rimmed baking sheet and toast for 6 to 8 minutes until aromatic. Let cool; roughly chop 1 cup and set aside remaining whole halves.

In a light-colored saucepan over medium heat, melt 1 stick (1/2 cup) unsalted butter. Swirl continuously as it foams and sizzles for 4 to 5 minutes until golden brown specks appear on the bottom and a nutty hazelnut aroma develops. Immediately pour browned butter and toasted specks into a heatproof bowl to cool for 10 minutes.

Roll chilled pie crust into a 9-inch deep-dish pie plate, crimp decorative edges, line with parchment paper, and fill to the brim with pie weights or dried beans. Bake at 375°F (190°C) for 12 to 14 minutes. Remove weights and parchment, brush bottom lightly with beaten egg white, and bake 3 minutes more to seal the crust. Cool.

Reduce oven temperature to 350°F (175°C). In a large mixing bowl, whisk together the cooled browned butter, dark brown sugar, maple syrup, lightly beaten eggs, vanilla extract, bourbon, flour, and fine sea salt until smooth, glossy, and emulsified.

Scatter the 1 cup of chopped toasted pecans across the bottom of the warm pie shell. Pour the brown butter custard gently over the nuts.

Carefully arrange the remaining 1.5 cups of whole pecan halves on top of the custard in elegant concentric circular rings, covering the surface completely.

Tent pie edges with a foil shield. Bake at 350°F (175°C) on the lower-middle oven rack for 50 to 55 minutes until the custard edges are puffed and set, and the center has a gentle, subtle jiggle when nudged.

Cool pie completely on a wire rack at room temperature for at least 4 hours. The custard will finish setting into clean, bakery-sharp slices as it cools. Serve with bourbon whipped cream and flaky sea salt.