Heat oven to 400º. Spray a pie pan (preferably deep dish) with non-stick spray. Peel and thinly slice the sweet potatoes, then cover the bottom and sides of pie pan with the slices. Sprinkle with a small amount of salt. Bake 20 minutes and check. Continue to bake until potato slices are soft enough to press into bottom and sides of pan, but not until they are falling apart. Reduce heat to 375º.
While sweet potatoes bakes, heat a large sauté pan over medium high heat. When hot, add fat (oil or butter). Swirl the pan, heat the oil, then add the chopped or sliced mushrooms and minced chard stems if using. Cook until soft and fragrant, adding salt and pepper to taste. Reduce heat to medium if desired (in case you want the mushrooms to cook less). After about 5 minutes, add sliced garlic. Add shredded chard leaves at this point if desired; cook 2 minutes.
Whisk eggs with milk and cheese(s); add chard leaves if you did not sauté them with the mushrooms. Add salt and pepper to taste if desired.
When sweet potato crust is finished, add mushrooms in a layer, then pour egg mixture on top. Bake at 375º until eggs are set; check at 20 minutes, then continue to bake as needed. Let stand 5 minutes out of the oven, then slice and serve.