Preheat the oven to 375°F and place a rack in the center position.
If your butter is not already melted, melt 3 Tbsp butter and let it cool slightly.
In a large bowl, whisk 3 large eggs and 1/2 cup sugar until smooth.
Whisk in 1 cup maple syrup, the 3 Tbsp melted butter, 1/2 tsp vanilla, and 1/4 tsp salt until the mixture is homogeneous.
Stir in 2 cups pecan halves until they are evenly distributed in the filling.
Place the 9-inch frozen deep-dish pie crust on a baking sheet. Pour the filling into the frozen crust and smooth the top.
Bake on the center rack for 30 to 40 minutes, until the filling is mostly set and the center is only slightly jiggly. If the crust or pecans brown too quickly, tent the pie loosely with foil.
Remove the pie from the oven and cool on a wire rack for 1 hour.
After cooling, store the pie in the refrigerator.