For the crust, whisk the flour, sugar, salt and baking powder in a 9-inch pie dish.
Whisk the milk and olive oil in a measuring cup and add the liquid to the pie dish. Toss with a fork to blend. When the dough is mixed, form it into a ball and pat it into a disk.
Press down the dough evenly into the bottom and up the sides of the pie dish to form a crust. Crimp the edges with two fingers.
For the filling, melt your butter in a small pan on the stove over medium-high heat. While it's melting, crack your eggs into a small mixing bowl. Add your sugar and pecans to the bowl.
Add the melted butter to your filling mixture. Squeeze in the juice from half a lemon. Add your lemon extract and salt.
Use a fork to stir your filling ingredients until combined. Pour the filling into your unbaked pie crust.
Bake the pie for 50-52 minutes, until the top is set and starting to brown. Let the pie cool on a wire rack. When it's no longer hot, chill it in the refrigerator to let it set before serving.
Serve the pie chilled. It's even better the next day. Garnish with extra pecans, if desired. Store leftovers in the refrigerator for up to five days.
I've always made this with pecan halves, since that's what I keep in stock, but it would probably be easier to slice the pie if you use the smaller pecan pieces. Pie filling adapted from Ruby Jones' recipe in American Pie: Slices of Life (and Pie) from America's Back Roads, Perennial Books, 2003, via the Plain Dealer. Crust adapted from King Arthur Flour.