Preheat grill to medium heat, approximately 350-400℉, and gather all the recipe supplies.
Mince the garlic and chop the basil, thyme and rosemary.
Brush grill grates clean, and set a 12" cast iron skillet on top to heat.
To the skillet, add crushed tomatoes, oil, garlic, basil, thyme, rosemary, salt and pepper. Stir to combine.
Close the grill lid, and let the sauce simmer for 15 minutes. Open lid periodically to stir the sauce.
Using a large spoon, make a shallow well in the tomato sauce, and crack or pour an egg in the divot. Repeat for remaining eggs. Close the grill lid.
Cook until yolks begin to cloud over and the whites are set as desired, about 10 minutes.
Scoop eggs and tomato sauce over thickly-sliced, toasted bread. Top with cheese, and season with salt and pepper, if desired. Serve hot.