Start by whisking the brown sugar and cornstarch together directly in your saucepan, off the heat. Doing this first keeps the cornstarch from clumping once liquid hits it. Make sure there are no dry pockets left before you move on, since lumps here mean lumps in your finished filling.
In a separate bowl, beat the egg yolks with the water and a pinch of salt until smooth and pale. Whisking them on their own first prevents scrambled bits from forming once they hit the hot pan later. Pour this mixture into the saucepan with your sugar and cornstarch, along with the chopped pecans.
Place the saucepan over medium heat and stir constantly as it warms. The mixture will gradually thicken into a glossy, pudding-like custard, usually within 5 to 7 minutes. Once it starts bubbling, let it boil gently for a full minute, still stirring, so the cornstarch fully activates.
Pull the saucepan off the heat right after that one-minute boil. Stir in the butter until it melts completely into the warm filling, then add the vanilla extract. Finally, fold in the reserved pecan halves so they're evenly distributed through the custard.
Pour the warm filling into your premade pie crust, spreading it out with a spatula so it sits level. Working quickly here helps the filling settle smoothly before it starts to firm up. Tap the pie dish gently on the counter to pop any air bubbles.
Transfer the pie to the refrigerator and let it chill for at least 2 hours, though overnight is even better. This chilling step is what replaces baking, allowing the cornstarch and egg yolks to fully set the filling. Slice and serve once it's firm to the touch.