Set up your barbecue for direct cooking. Place a small Weber Ware Frying Pan on the barbecue, close the lid, and preheat your barbecue for direct cooking. Please refer to your handbook for further instructions.
Remove the rind from the speck and chop into 1cm cubes.
Once the barbecue is preheated, adjust the burner control(s) to medium. Fry the speck in the pan, with the lid closed, for 5 minutes, stirring occasionally. Remove the pan from the grill and set aside to cool slightly.
Set up your Q for indirect cooking, with a convection tray and trivet. Make adjustments to the burner control(s) for roasting. Please refer to your handbook for further instructions.
Pour the marinara sauce into the pan, on top of the fried speck. Crack 4 eggs on top of the marinara. Season the eggs with salt and pepper. Sprinkle the top with shaved Parmesan cheese. Return the pan to the barbecue and cook on the indirect roasting setting, with the lid closed, until the eggs are cooked to your liking, 15 to 20 minutes. Butter both sides of the bread and toast directly on the grill for 1 minute on each side.
Roughly chop the basil and sprinkle over the baked eggs. Serve the baked eggs warm with the toast.