Preheat oven to 375ºF.
Place a medium pot over medium heat and melt the butter. Sprinkle the flour over the melted butter and cook for about a minute. Slowly whisk the milk into the butter-flour mixture and season with salt, pepper and nutmeg. Let it thicken a couple of minutes then stir in about a cup of the Parmigiano. Set the sauce aside.
Place a large, cast iron skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Toss in the cracked clove of garlic and cook for a minute or two to release its aroma and flavor. Add in the chard and wilt it down, about 2 minutes, then wilt in the spinach a few handfuls at a time. Season the greens with salt and pepper.