Heat olive oil in a large cast-iron or ovenproof nonstick skillet over medium-high heat. Reduce heat to medium, add onions and cook, stirring occasionally, until they are tender and light golden brown, 15 to 20 minutes. Stir in water and thyme, scraping up any browned bits.

Meanwhile, position rack in middle of oven; preheat to 450 degrees F.

Blend flour, milk, eggs, egg whites, canola oil, sugar, salt and pepper in a blender until smooth. Pour the batter over the onions. Sprinkle with cheese.

Bake the pancake until puffed and golden, about 15 minutes.

Meanwhile, combine vinegar and honey in a small saucepan. Bring to a boil over medium-high heat and cook until syrupy and reduced to 1/3 cup, 12 to 15 minutes. (Watch carefully during the last few minutes to prevent burning.) Cut the pancake into wedges and serve immediately with the balsamic syrup.

Kitchen Tip: Onions contain a volatile compound called lachrymator that reacts with the fluid in your eyes and makes them water. To chop them without crying, try wearing goggles, burning a candle nearby or cutting them under cold water. To mellow the bite of a raw onion, soak it for an hour in 1 cup cold water, 1/4 cup vinegar and 1/2 teaspoon salt and then rinse thoroughly.