Preheat the oven to 425°F.
Place the mushroom caps on a rimmed baking sheet, stemmed-side down so the liquid drains away from the mushrooms as they start to shrink. Drizzle with 1 tablespoon of the oil and season with salt and pepper. Roast until tender, 10-12 minutes. Remove from the oven.
Meanwhile, chop the reserved mushroom stems. In a small skillet, heat 1 tablespoon of the oil, 1 turn of the pan. Add the mushroom stems and brown; add the onion and garlic, season with salt and pepper, and cook to soften. Let cool, then transfer to a food processor. Add the spinach and artichoke hearts. Season with salt, pepper and nutmeg, and pulse-chop. Pulse in the remaining tablespoon of oil, the Parm, egg yolks, pine nuts, and cream. Transfer to a bowl.
Flip the cooked mushroom caps over and fill them with the spinach-artichoke mixture, mounding it up a bit. Bake until the filling is cooked through, 12-15 minutes.