Heat the oven to 350 degrees. Line a 9-inch pie pan with crust, then crimp the edges decoratively, or press them flat with the tines of a fork.
In a medium saucepan, melt the butter over medium heat, swirling now and then to melt it evenly and quickly. Meanwhile, in a medium bowl combine the brown sugar and flour, and use your hands or a large spoon to combine them well.
When butter is melted, add brown sugar and stir well, scraping and scooping and pressing to combine everything into a thick, soft mixture, resembling fudge. Remove the pan from the heat and set aside.
In a large mixing bowl, combine the milk, eggs, and vanilla. Stir with a fork or a whisk to mix everything together well. While stirring gently, slowly scrape the thick, warm brown sugar mixture into the milk mixture. Mix, stir, and press, using a whisk or a large fork or spoon, to combine everything evenly and well.
Add the black walnuts and stir well. Pour the filling into the piecrust and place filled pie in oven. Bake until the filling puffs up and cracks a little, and the center is fairly firm, wiggling only a little when you gently nudge the pan, about 40 to 50 minutes. Place the pie on a cooling rack or a folded kitchen towel and let cool for at least 30 minutes. Serve warm or at room temperature
*Note: Look for shelled black walnuts in 1 1/2 cup packages (8-ounces) in the produce section of area grocery stores.
Adapted from Southern Pies by Nancie McDermott