In a food processor or mixer, blend together the flour and eggs until smooth. Mix in the sugar and vanilla and blend well. Finally slowly add the milk and mix well to make a smooth batter. Let the batter sit for 30 minutes to an hour.
In the microwave, melt the butter in the bottom of a two quart or so baking dish. Tip the pan and swirl the butter so that it coats evenly the bottom and sides. Pour the batter into the pan and add the floured prunes (the flour should help to keep the fruit from sinking to the bottom, but if they are large, they'll sink anyway. Don't worry, it still tastes great).
Bake for 30 minutes at 400° F. Turn the oven off and leave the cake in the oven for 30 more minutes.
We like this prune cake recipe best when warm, maybe two hours after it has come out of the oven. However, it is also good cold and makes a nice breakfast if you have leftovers. You can sprinkle the top with powdered sugar after the far has cooled some.