Preheat oven to 400F.
Heat about 1 tablespoon EVOO, 1 turn of the pan, in large skillet over medium heat. Add pancetta and lightly brown. Add onions and gently soften and sweeten, 20 minutes or so. Season with salt and pepper, sprinkle with sugar and stir a minute more. Transfer to a plate and reserve.
Add remaining EVOO to pan and raise heat to medium-high. Add mushrooms and brown 7-8 minutes. Season with nutmeg, salt and pepper, and deglaze pan with Marsala. Stir in walnuts, figs and reserved onions. Turn off heat and gently arrange the ingredients on the bottom of a parchment paper-lined, straight-sided 9-inch cake pan. Press down lightly with a spatula to set in place. Top the onions, mushrooms and figs with sage or rosemary and cheese.
Cut a round of puff pastry slightly larger than the pan and set dough on top of ingredients. Tuck in the edges and bake 25 minutes. Let stand 5-10 minutes more then invert on serving dish. Cut into 4 large wedges and serve with a spinach salad with a grainy Dijon and honey vinaigrette alongside.