1. Prepare the grill for direct cooking over medium heat (350° to 450°F).
2. Crack all the eggs gently into a large bowl. Butter the bread slices on both sides.
3. Brush the cooking grates clean. Arrange the bacon in a single layer in a 12-inch cast-iron skillet, with pieces on the bottom and around the sides. Grill over direct medium heat, with the lid closed as much as possible, until crisp, 15 to 20 minutes, turning and rearranging the bacon as it cooks and shrinks. Drain the bacon on paper towels and then wrap in foil and keep warm on the grill’s warming rack or in a low oven.
4. Use a large serving spoon to scoop out about half of the bacon grease from the skillet, leaving a ⅛-inch layer on the bottom. Gently pour all the eggs into the skillet at once and season with the salt and pepper. Place the bread directly on the grill and cook both the eggs and the bread over direct medium heat, with the lid closed as much as possible, until the eggs begin to cloud over on top (the yolks will be partially runny) and the bread is toasted. The eggs will take 4 to 6 minutes and the toast will take 3 to 4 minutes. Turn the bread once during grilling. Transfer the toast to the warming rack or oven with the bacon.
5. Using a serving spoon or spatula, cut the eggs apart and scoop them out of the skillet one at a time. If savory toast is desired, rub each side with the cut side of the garlic clove while the toast is still warm. If sweet toast is preferred, spread it with jam. Serve the eggs and toast immediately with the bacon.