What is the function of this shallow, 19-divoted, eared cast iron piece?
They look like the Dutch "mini pancake" pans... they're used to make poffertjes.

There are nearly identical pans on sale here.

The Wikipedia article talks about them more specifically:


  Poffertjes are a traditional Dutch batter treat. Resembling small, fluffy pancakes, they are made with yeast and buckwheat flour. Unlike American pancakes, they have a light, spongy texture. Typically, poffertjes are served with powdered sugar and butter, and sometimes syrup or advocaat.


And an image from a recipe page: