Preheat your oven to 350°F (175°C). Prepare your 9-inch pie crust in a pie plate, crimping the edges for a decorative finish.
Spread the pecan halves in a single layer on a baking sheet and toast in the preheated oven for 6 to 8 minutes until fragrant. This enhances the nutty flavor.
In a large mixing bowl, whisk the 3 large eggs until lightly beaten. Add the pure maple syrup, brown sugar, melted butter, vanilla extract, salt, and all-purpose flour. Whisk until the mixture is completely smooth and the sugar has mostly dissolved.
Arrange the toasted pecan halves evenly across the bottom of the prepared pie crust.
Slowly pour the maple egg mixture over the pecans, ensuring they are well coated and the liquid is distributed evenly.
Place the pie on the center rack of the oven. Bake for 45 to 55 minutes. The pie is done when the edges are puffed and set, and the center has a slight, jelly-like jiggle but is not liquid.
If the crust edges begin to brown too quickly before the filling is set, loosely cover the edges with a pie shield or aluminum foil strips.
Remove the pie from the oven and place it on a wire cooling rack. Allow the pie to cool completely at room temperature for at least 4 hours. This step is critical for a corn-syrup-free pie to set properly before slicing.