Begin by creaming the softened butter and sugars in a large bowl until the mixture is light and fluffy, which should take about 5 to 7 minutes. Next, incorporate the egg and vanilla extract, mixing thoroughly. In a separate bowl, combine the flour, baking soda, and salt. Gradually add this dry mixture to the creamed ingredients, stirring until fully integrated.
Spoon approximately two tablespoons of the dough into each of the twelve paper-lined muffin cups, filling them halfway. Bake in a preheated oven at 375°F for around 10 minutes or until the edges turn light brown.
While the initial baking is taking place, prepare the filling by beating together the packed brown sugar, egg, and salt in a small bowl for about 5 minutes, until the mixture appears lighter in color. Fold in the semisweet chocolate chips and chopped walnuts.
After the cupcakes have partially baked, remove them from the oven. Carefully spoon rounded tablespoonfuls of the filling into the center of each cupcake. Return to the oven and bake for an additional 12 to 14 minutes, or until they are a deep golden brown. Allow the cupcakes to cool for 10 minutes in the pan before transferring them to a wire rack to cool completely.