Prepare the pastry. On a lightly floured work surface, roll out the pastry to a circle just under ¼ inch (6 mm) thick. Dust the bottom of a 9-inch (23 cm) glass pie plate with flour and line it with the pastry. Trim, tuck and crimp the edges of the pastry shell and chill for at least an hour.
Preheat the oven to 400°F (200°C).
Brown the butter. Melt the butter in a saucepan over medium-high heat and let it cook, stirring occasionally, until the bubbling subsides and the butter itself turns a rich nutty colour, about 5 minutes. Set aside to cool for 10 minutes.
Make the filling. Whisk the brown sugar, maple syrup, corn syrup, whipping cream, lemon juice (or vinegar), vanilla and salt together until well combined. In a separate bowl, whisk the eggs, then add them to the sugar mixture and whisk until blended. Pour in the brown butter and whisk well. Toss in the pecans, stirring to coat them completely, and pour the filling into the pie shell.
Bake the pie on a baking tray for 10 minutes, then reduce the oven tempera- ture to 375°F (190°C) and bake for another 30 to 35 minutes, until the pie filling starts to soufflé around the outside edge. The centre will still be jiggly. Cool the pie on a rack to room temperature before serving.