In a bowl, combine the flour, sugar, baking soda, and salt.
In a 1-cup measuring cup, put two eggs, then add milk until it almost reaches the top (approximately 1/2 c; depends on the eggs).
I make this by hand the way she always did, so I'm not sure if using a mixer would be beneficial. Mix for 5 minutes with the dry ingredients.
For 12 to 15 minutes, spread evenly in a greased 9 x 13" pan, and bake the cookies until they are fluffy, golden brown, and cooked through.
While waiting, make a powdered sugar icing by mixing 1 cup powdered sugar with a little milk (start with just a tablespoon or so). Mix well. When necessary, add milk to achieve the desired consistency (a bit like a glaze).
Crush the peanuts into a powder.
After baking, let cookies cool completely before cutting into squares. Roll in nuts after coating with frosting. Put wax paper down to dry.