Preheat the oven to 400°F. Grease a shallow 2‐quart gratin dish or oblong baking pan with a little olive oil.
Put 2 tablespoons of the oil in a large, deep skillet over medium‐low heat.
Add the garlic and sugar and cook, stirring occasionally, until the garlic is soft, plump, and starting to color, about 10 minutes
Turn off the heat and add the arugula.
Sprinkle with salt and pepper, toss gently once or twice, and spread the leaves into the bottom of the prepared dish.
Drizzle with the vinegar.
Slice polenta into ½‐inch‐thick slices; sprinkle with salt and pepper to taste.
Carefully spread them out on top of the arugula, overlapping them a little if necessary.
Drizzle with the remaining oil and sprinkle with the cheese.
Bake until the topping is golden and bubbling, 20 to 25 minutes.
Serve, topped with lots of black pepper.