Heat the oven to 450 degrees F. Put a large pot of water on to boil. In a 9x13-inch Pyrex baking dish, toss the 3 cups vegetables with 2 tablespoons of the oil and 1/4 teaspoon salt and spread in one layer. Roast until the vegetables are well browned and shrunken, 28 to 30 minutes, stirring occasionally with a flat metal spatula.

After the vegetables have roasted for about 15 minutes, add 2 teaspoons salt and the tortellini to the boiling water; cook the pasta until tender. Save some of the water to pour into two large shallow soup bowls to warm them. Drain the tortellini in a colander. In a small saucepan, heat the remaining 1 tablespoons oil over medium heat. Add the shallots; saute until softened and browned, about 2-1/2 minutes. Stir in the chile flakes and add the chicken broth. Bring to a simmer, cover, and simmer for 4 to 5 minutes. Turn off the heat and keep covered. Pour the water out of the soup bowls. Divide the tortellini between the warmed bowls. Spoon the roasted vegetables over the pasta. Pour the broth over the vegetables and garnish with the Parmigiano and parsley. Season with salt and pepper to taste. Serve with a lemon wedge.