Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch pie dish.
Place the brown sugar and butter in a mixing bowl, and beat them together with an electric mixer until creamy and very well combined, without lumps. Beat in eggs, one at a time, incorporating the first egg before adding the next one. Add the vanilla extract and salt; beat the flour in, a little at a time, and then the milk, making a creamy batter. Pour the batter into the prepared pie dish.
Bake in the preheated oven for 35 minutes; remove pie, and cover the rim with aluminum foil to prevent burning. Return to oven, and bake until the middle sets and the top forms a crusty layer, about 15 more minutes. Let the pie cool to room temperature, then refrigerate for at least 1 hour before serving.
A / B / C / D / E / F / G / H / I / J / K / L / M / N / O / P / Q / R / S / T / U / V / W / X / Y / Z