Place the mushrooms in an ovenproof dish, drizzle with 2 tablespoons of the olive oil, place a thyme sprig in each and pour the marsala around the mushrooms. Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 15–18 minutes.
Meanwhile, heat the remaining olive oil in a frying pan and cook the pancetta for 4–5 minutes, until browned and just starting to crisp. Stir in the chopped chestnuts and spinach and stir until the spinach has wilted. Season well.
Remove the mushrooms from the oven, spoon the filling into each one and top with the grated mozzarella. Return to the oven, or cook under a preheated hot grill for 5–6 minutes, until the cheese is melted and golden.