Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking pan.

Make the oatmeal batter: Combine oats, flour, baking soda, and salt in a bowl.

Beat brown sugar and butter with an electric mixer in a large bowl until fluffy. Mix in eggs and vanilla. Stir in flour mixture until combined.

Make the filling: Heat condensed milk, chocolate chips, butter, and salt in a medium saucepan over low heat, stirring frequently, until smooth, 5 to 8 minutes. Remove from the heat and stir in walnuts and vanilla.

Pat 2/3 of the oatmeal batter into the bottom of the prepared pan. Spread filling evenly over top, then dot with remaining batter.

Bake in the preheated oven for 30 to 35 minutes. Remove to a wire rack and let cool completely before cutting into 24 bars.