Make the stuffing by melting the butter in a small frypan over medium heat. Once melted add the shallots, and season with salt and pepper. Cook the shallots for a couple of minutes or until they become translucent. Remove from the heat and set aside to cool slightly. In a medium bowl, mix all the stuffing ingredients together, including the shallots. Fill each mushroom with a spoonful of mixture.
To prepare the Pulse for direct cooking over medium-high heat (240°C-260°C), preheat the barbecue by turning the control knob(s) to high. Preheat until the barbecue reaches at least 260°C, which will take approximately 15 to 20 minutes with the lid closed.
Once the barbecue is preheated, open the lid and brush the cooking grills clean. Adjust the control knob(s) to one notch greater than medium for direct cooking over medium-high heat.
Lightly coat the stuffed mushrooms with oil, and season with salt and pepper. Cook the mushrooms directly on the grill for 10-12 minutes or until the mushroom is cooked through, and the stuffing has reached an internal temperature of 71°C. Remove from the barbecue and set aside.
Place the Pulse griddle in the centre of the cooking grills and preheat over direct high heat for 10 minutes. Lightly grease the egg rings with oil. Once preheated place the egg rings on the griddle. Crack an egg into each ring, and season with salt and pepper. Cook the eggs for 3-5 minutes or until cooked to your liking. Once the eggs are cooked remove from the barbecue.
While wearing heat tolerant gloves, remove the hotplate from the barbecue. Return the mushrooms to the cooking grill to reheat. While the mushrooms are reheating, cook the bacon for 2-3 minutes, turning once. Serve with crusty bread and tomato chutney.