This frittata is meant to be thin, with just enough egg to bind the filling. Sunchokes are also known as Jerusalem artichokes. Roasting them brings out their nutty essence. Yukon Gold potatoes can be substituted.
Preheat oven to 500 degrees. Toss together sunchokes, bay leaves, 3 tablespoons oil, and garlic on a rimmed baking sheet. Season with salt and pepper. Roast until tender and dark golden-brown around edges, 15 to 20 minutes. Discard bay leaves. (Leave oven on.)
Bring a pot of salted water to a boil. Add Swiss chard, and cook until tender, about 5 minutes. Drain; let cool slightly. Squeeze out excess liquid.
Whisk eggs with 1/4 teaspoon pepper, the Parmesan, and scallions in a bowl. Heat remaining tablespoon oil in a 12-inch ovenproof skillet over medium-high heat. Add sunchokes and Swiss chard, and spread on bottom of skillet. Add egg mixture, filling in spaces between vegetables. Swirl to distribute (eggs will not cover vegetables completely). Cook, shaking skillet occasionally, until sides are set, about 2 minutes.
Transfer to oven, and bake until puffed and center is set, 4 to 5 minutes. Place a large platter over skillet, and invert. Serve hot, warm, or at room temperature.