This lasagna is slightly unconventional, but not so mush that traditional lasagna lovers wont love it. The caramelized onions have a delicious sweetness that is offset by the robustly flavored chard. In large pot of boiling salted water, cook noodles until just tender, about 8 minutes for dried and 1 minute for fresh. Drain and rinse under cold water.

Spread noodles on clean kitchen towels and cover with plastic wrap. In large skillet, heat 1 tablespoon oil over medium heat. Add garlic and cook, stirring often, 30 seconds. Add chard and cook, stirring often, until tender, about 5 minutes. Transfer chard to medium bowl and stir in ricotta cheese. Season with salt and pepper. Set aside. Wipe out skillet, heat remaining 3 tablespoons olive oil over medium heat. Add onions and cook, stirring, until onions begin to brown all over, about 15 minutes. Sprinkle with sugar and stir.

Cook, stirring, until deep amber in color, about 20 minutes more. Remove from heat and splash with vinegar. Set aside. In medium saucepan, heat 2 1/2 cups milk over medium heat until steaming. Meanwhile, put flour in small bowl and whisk in remaining 1/2 cup milk until smooth; whisk into hot milk mixture and whisk constantly until sauce comes to a simmer and thickens. Continue cooking and stirring for 1 minute. Stir in Asiago or Parmesan cheese until melted and smooth. Season with salt and pepper. Preheat oven to 400 F. Lightly oil a 9 x 13-inch baking dish or coat with non-stick cooking spray.

Coat bottom of prepared dish with 1/2 cup of sauce. Line bottom with a single layer of noodles. Spread half the chard over the noodles. Add another layer of noodles, arrange caramelized onions on top and sprinkle with salt and pepper. Spread another 1/2 cup sauce over all. Add another layer of noodles, followed by the remaining chard mixture. Finish with remaining noodles and sauce.

Sprinkle with remaining Parmesan. Lightly oil a large piece of aluminum foil or coat with nonstick cooking spray and use it to tightly cover dish. Bake lasagna for 30 minutes. Uncover and bake 10 to 15 minutes more, or until lightly browned and bubbling. Let stand for 10 minutes before serving.