Charred Eggplant Omelet

We had an electric stove when I was growing up, and my mom used to put eggplant right on top of the glowing red coils and pinch the stems to turn them. I helped by peeling off the charred skin, mashing the flesh, and dipping it in egg. The result was a kind of omelet, typically layered with ground beef. My mom liked to fry the eggs hard, until they were speckled brown, with crispy lace at the edges.

The version I make now is almost vegetarian—save for a seasoning of fish sauce—and i