Preheat your oven to 350°F (175°C). Roll out the pie dough and fit it into a 9-inch pie plate. Chill the crust in the refrigerator for about 15 minutes.

Chop the walnuts and toast them in a sauté pan over medium heat for about 5-6 minutes or until golden brown.

Melt unsweetened chocolate in a heat-safe bowl over simmering water, stir gently until melted, then cool slightly.

Stir granulated sugar into the melted chocolate until fully incorporated. Add unsalted butter and vanilla extract, mixing until smooth.

In a large bowl, sift together all-purpose flour, baking powder, and salt.

Beat softened butter on medium speed for 2-3 minutes. Gradually add the sugar mixture, then mix in egg (or flax egg) and milk, alternating with dry ingredients.

Pour the vanilla cake batter into the chilled crust, then spoon the chocolate mixture on top without stirring.

Sprinkle toasted walnuts over the chocolate layer. Bake for about 45 minutes or until a toothpick comes out clean.

Let the pie cool for at least 30 minutes on a wire rack before slicing and serving.