Preheat the oven to 350°F (180°C). Butter and flour a 12 x 7 x 2-inch pan. If using a glass pan, preheat the oven to 325°F (165°C).
In a large bowl, beat together the butter, sugar, egg yolk, and vanilla until smooth and creamy.
Add the oats, flour, and half of the walnuts.
Beat just until blended; do not overwork the dough. You may need to finish this step by hand.
With a rubber spatula or your fingers, spread the mixture evenly into the prepared pan and smooth the top.
Bake for 25 minutes, or until it is a rich golden color.
Remove the pan from the oven and immediately sprinkle on the chocolate chips. Return to the oven for 3 minutes, or until they are soft. With a spatula, spread the chocolate evenly over the surface.
Sprinkle on the remaining nuts and press them lightly into the surface.
Cool on a wire rack for 30 minutes, then chill for 1 hour, or until the chocolate is firm but not hard.
Cut into 24 bars and serve. Store in a tightly covered tin.
Don't overbake the base. It should be golden brown at the edges but still slightly soft in the center when you remove it from the oven; it will firm up as it cools.