I found this delicious little recipe on In My Kitchen. The author of that blog recounts her childhood memories of having this as part of a Utah school lunch. I am a native Utahn, and don't remember having them for lunch in elementary school (although I do remember some incredible peanut butter cookies, the only peanut cookies I would eat at that point in my life). But they are awfully good.
Warning: this recipe makes a lot of cookie bars. It's baked in a jelly roll pan, which we call a cookie sheet at our house. It's something like 16 x 9. So either make it when you're going to a very large gathering, or plan on having it around for a few days. I made it on Monday of this week (which was spring break), and we still had lingering leftovers by Thursday. It holds up well over time, though, and the kids were in heaven with readily available snacks all week.
Peanut Butter Fingers
3/4 cup butter or margarine
3/4 cup brown sugar
3/4 cup sugar
Cream these ingredients together and then add:
3/4 cup peanut butter, cream until smooth
Note: We used creamy peanut butter because we had a surplus of it and because the kids prefer chunky on their sandwiches. But I think chunky PB would work great, and would add a little nuttiness to the mix.
3/4 teaspoon baking soda
1 1/2 teaspoons vnilla
1/2 teaspoon salt
1 1/2 cups oats
1 1/2 cups flour
Mix together and pat down into a jellyroll pan. Bake at 350 degrees for 15 minutes.
Let the cookie substance cool a little, but while it is still warm, spread a think layer of peanut butter over the top. After it has cooled quite a bit, add the frosting on top:
6 tablespoons butter
1 1/2 teaspoons vanilla
4 3/4 cups powdered sugar
1 tablespoon cocoa
1/4 cup milk
Blend frosting until smooth and spread over cookies.