Heat oven to 350 degrees F. Oil a 2 1/2- to 3-quart baking dish. Heat the oil in a large skillet over medium heat. Add the onion, season with 1/4 teaspoon each salt and pepper and cook, covered, stirring occasionally, for 4 minutes. Add the chard stems and cook, covered, stirring occasionally, for 4 minutes. Add the chard and cook, tossing occasionally, until wilted, about 3 minutes. Meanwhile, in a large bowl, whisk together the eggs, milk and 1/2 teaspoon each salt and pepper. Add the bread and let sit, tossing occasionally, for 5 minutes. Fold the chard mixture, artichokes and ham into the bread mixture, then add the goat cheese. Transfer the mixture to the prepared baking dish, sprinkle with the Parmesan, and bake until set and a knife inserted in the center comes out clean (cover with foil if it browns too quickly), 45 to 50 minutes. Serve with salad, if desired.